Your moves:

The only Devil Arm the game allows you to equip for the Mundus 2 battle is Sparda, but Roundtrip, Air Hike and Stinger will transfer over if you have already bought them for Alastor. Air Raid and Vortex won't transfer across, probably because Alastor DT would conflict unacceptably with Sparda DT. Or something.  

You do have a couple of altered, if not actually new, moves. Namely:  

Meteor - You use the Square button to send out Meteors - keep tapping it to send out uncharged ones; keep it held down to charge up a Meteor. You can only charge up Meteor if you have Ifrit's Meteor Lvl 2 ability. I'm not sure if you need Ifrit's Meteor Lvl 1 ability to do uncharged Meteors or not - sorry :-/  

DT mode - In DT mode, the Sparda sword turns into a giant, flaming red, sword. The sword combos are stil the same, though.  

Mundus 2's Attacks: 

[Spinning Spheres]

You'll come to love the spinning spheres almost as much as Mundus 1's lasers. *rolls eyes*. Anyway, there are four different formations, but the telegraph for all of them is identical: Mundus rests his right hand on his hip and motions upwards with his left hand, jabbing a finger into the air. 

1. Beige spheres: "one-by-one" - Mundus summons a total of 5 beige spheres, which appear one after the other. A beige sphere appears, is still for a second, then starts spinning around, sending out two waves of lasers as it does so. Get rid of each beige sphere with a single shotgun shot (two shots on Hard/DMD mode). 

2. Beige spheres: "six-in-a-row" - Mundus summons a horizontal row of six beige spheres, which appear along the centre of the platform. They remain still for a while, then travel one-and-a-half times around the battlefield - any you didn't destroy the first time will pass by you one more time before finally evaporating. To destroy them, run to stand in between the 3rd and 4th spheres (Dante will always be smack bang in the middle of the row when it first appears). Then fire 1-2 shotgun shots in both directions. You can get rid of all six spheres this way, but even if you don't, you'll get rid of the majority. Also, if you get to the very front of the platform, then the lasers can't hit you as the beige spheres move out - just watch out for them on their return!  

3. Beige spheres: "crown-of-spheres" - Mundus summons six beige spheres, which surround the top of his head in the shape of a crown. The beige spheres don't do anything for a long time, but will finally start to send out streams of white lasers. You can easily get rid of the spheres before they become dangerous, by standing at the back of the platform and shooting away with the shotgun. 

4. Dark Spheres - These are different to the beige spheres, but are summoned in the same way. Mundus summons 4 large dark green spheres and places them at equal distances from each other around the battlefield. On their own, they don't do anything, but eventually Mundus will gather them up and convert them into white fireballs, which he then slings at you. (More on this later.) You can destroy the dark spheres for 3.5 DT runes each, but I wouldn't go out of your way to destroy more than one or two.  

[The rest of Mundus's moves]

Magma Waves - Mundus scoops his hand over the lava and sends a paper-thin wave of magma towards you. Most of the time he will send two magma waves in a row, but sometimes he only sends one. The waves are easy to evade with a roll or jump to the side, or even just by holding down R1 and walking - the main danger lies in the speed they come out at. Try not to get caught out by them when attacking Mundus.  

Strafing Lasers - Mundus moves his right arm right to left across the battlefield, index finger pointing, sending strafing lasers as he does so. Do a jump or Air Hike to the right over the lasers as they reach you. You can also roll under them, but generally it's safer to jump over them. 

Laser Rainstorm - *gibbers*. Hate... this... attack... Whoops, sorry, bad memories, heh :p ... Anyway, Mundus tenses up as though he had painful constipation, bends forwards and crosses his wrists in front of his face - a stream of large pink lasers go up into the sky and fall down across the battlefield like rain. This attack has poor accuracy, but wide coverage, and is impossible to evade 100% consistently. Your best bet is to start rolling or DT-running as soon as you spot the telegraph for the attack - and then just keep rolling or running ahead of the lasers. 

Rising Dragon - Mundus lifts both arms into the air, then bends over and slams both fists down into the lava - a couple of seconds later, a circle of flames will appear where Dante is, then a tall, skinny dragon will go shooting upwards into the sky. Jump/roll/run to the side as soon as you spot the telegraph for this attack. 

Lava Dragon - Not to be confused with the Rising Dragon, this is a different beast altogether; and an attack you'll probably come to love, since killing the lava dragon yields a large green orb. Mundus raises his right arm above his head, then plunges it into the lava to summon the lava dragon.

The lava dragon - a strange, antlered beast - destroys any rocks it touches as it makes its way through the lava towards you. Once it gets close enough, it will start sending fireballs at you. You can deflect a fireball with a non-DTed sword slash for an instant kill. Otherwise, just use DTed sword combos, charged Roundtrips, or a flurry of uncharged Meteors to kill the dragon. The one thing you shouldn't do is try to ignore it, as it lingers on forever otherwise - and eventually Mundus will go on to do other attacks.  

Lava Pillars - The telegraph for this attack is the same as for the Lava Dragon: Mundus raises his right arm above his head, then plunges it into the lava to summon the lava pillars - eight of them will arise from the ground, following you around. It's pretty much identical to Phantom's attack, and evaded the same way - just run or walk without doubling back.  

Rock Smash - First of all, Mundus swings his left arm out horizontally to smash up the "inner" rocks, then he draws his right arm back, clenches his fist, and leans forward to do a huge punch. The punch is aimed at you, but will smash any "outer" rocks in its path. Really easy to evade. Just Air Hike away if there are "outer" rocks in front of you. Otherwise, you can run to the front of the platform and move left so that you are slightly to the left of Mundus - his fist will miss, but you will get the chance to do a combo on his hand. You can also move to the back of the platform - again, Mundus's fist will miss, whilst in the meantime you can start charging up a Meteor or Roundtrip.  

White Fireballs - As mentioned earlier, Mundus will gather up the dark spheres and convert them into white energy, which manifests itself as white fireballs spinning around his head. He will release from 0-4 white fireballs, depending on how many of the dark spheres you destroyed. (Like a moron, Mundus will go through the motions of slinging the fireballs, even if there are no dark spheres to collect!) The fireballs are extremely difficult to consistently evade - your best bet is to roll along the edge of the platform, but this won't work every time. Instead, you can deflect them back to Mundus for lots of damage.

The fireballs travel towards you at different speeds, depending on how many there are - four are the slowest, one is the fastest. You never want to have to deflect all four - the only way of deflecting four fireballs is to use sword-cancelled slashes. Instead, 3 is the ideal number, as the 3-Hit combo works wonders here.  (Button-mash to do the 3-Hit combo.) Start your 3-Hit combo when the fireballs are about halfway between Mundus and you. Being in DT mode gives you more leeway, plus reduces the damage dealt should you get the timing wrong. As if that would happen... :p 

Meteors-from-the-sky (Red lifebar only) - I say red lifebar only, but this attack can actually be started up just before Mundus's lifebar goes into the red. At any rate, the telegraph is the same as for the Rising Dragon: Mundus lifts both arms up into the air, then bends over and slams his fists into the lava - about a second after straightening up, six (Normal mode) or 10 (Hard/DMD mode) Meteors will rain down from the sky, one after the other. Just keep on running or rolling along the platform to evade the meteors - you can do a U-turn if you reach the end of the platform before the attack is over. On its own, this attack isn't so bad - it's the hair-raising combinations that Mundus does along with it...  

"Stacked" Attacks: 

Just like Mundus 1, Mundus 2 can stack his attacks, and how. He can, at least on Hard/DMD mode (I'm less sure about Normal - sorry! :-/), stack any spinning spheres formation with any "main" attack e.g. Laser Rainstorm, Lava Dragon, etc. This means that you've got to evade both lasers, plus whatever else is going on at the same time. If Mundus does an attack which is capable of shattering the rocks, you've got to take into account the shattering fragments too :p 

As far as I remember, Normal mode Mundus does do stacked attacks, but they're easier to deal with overall because it takes fewer shotgun shots to get rid of the spinning spheres. 

Mundus 2's Patterns: 

It always helps to have an idea of what a boss is going to do. In Mundus 2's case, he attacks in cycles, each cycle beginning with the summoning of the floating rocks in the lava and ending with the gathering of the dark spheres/sending of the white fireballs. 

A typical cycle is as follows: 

- Floating rocks are summoned up from the lava

- 1 Dark Spheres + 1 spinning spheres (any formation) are summoned. They can be done in either order, but Dark Spheres will *always* be summoned, whether first or second

- Mundus will then do 2-3 "main" attacks, stacking them with spinning spheres attacks

- Finally, any leftover Dark Spheres will be summoned and converted into white fireballs, which also destroy any floating rocks in the vicinity

- The cycle begins anew 

That's pretty much it. However, Lava Dragon and Rock Smash can also act as cycle enders in their own right at any time, particularly the Lava Dragon attack. No matter when the lava dragon appears, Mundus will typically gather up the dark spheres shortly afterwards, although he may do a spinning spheres attack first. The Rock Smash attack can operate in the same way, but sometimes Mundus just does it as an ordinary attack as well (i.e. it doesn't force the early gathering of the Dark Spheres). 

The Battle

DT is fully restored for this battle. Dante always begins on the same spot - on the left of the two, fixed, adjacent platforms. There are three fixed platforms on the battlefield, but the third one can only be reached by travelling on a floating rock. It's best to stick to the two adjacent platforms - you can cross over to the other one with just a single jump. 

In order to get through this battle without items ('cos I'm sure that's your biggest aim, right? :p), you should try to learn all of Mundus's telegraphs. It will help you massively in knowing what to expect next. Where Mundus uses the same telegraph for two attacks, take evasive measures for the most appropriate attack, e.g., for lava pillars/lava dragon, start running until you are sure it's the lava dragon and not the lava pillars.  

You should also learn when you can attack Mundus. Simply put, you can generally safely charge up a Roundtrip or Meteor immediately after evading any one of Mundus's attacks - unless he starts up a "one-by-one" spinning spheres attack in the meantime, in which case break off your attack to deal with the beige spheres. Otherwise, Mundus's lava dragon and white fireballs give you the most prolonged opportunities to attack Mundus.  

And finally, equip the shotgun. It's by far and away the best gun for dealing with Mundus's frequent spinning spheres attacks. For Hard/DMD mode, the "shotgun-twitching" technique comes in massively helpful.  

There are two approaches which can be taken to the Mundus 2 battle: the first is a play-it-safe, long-range strategy from the fixed platforms, and the second is a more aggressive, short-range strategy from the floating rocks.  

For the first approach, Roundtrip becomes a must. It will become your principal attack, as well as a means of building DT when you have run out. The idea is to send charged Roundtrips/Meteors whenever you can. This isn't as easy as it sounds, since much of the time you'll be evading Mundus's many attacks and shooting at beige spheres. Even when you're not, the floating rocks will often get in the way. If you go to the back of the platform, a Roundtrip or Meteor will go over an "outer" floating rock, but an "inner" one will block it. Make full use of the two adjacent fixed platforms to find plenty of free space for attacking Mundus.  

If you think that Mundus is likely to gather the dark spheres soon, start searching for a clear space in the lava between you and him - you don't want there to be any floating rocks in front of you when he sends the white fireballs. If you do get caught out,  then DT to minimize damage, 'cos chances are, you're not escaping white fireballs and rock fragments unscathed.  

Sometimes, after gathering the dark spheres, Mundus summons a spinning spheres formation - if it's the "one-by-one" formation, shotgun-twitch away until all the spheres are destroyed. It's less bad on Normal mode, but on Hard/DMD, you will only just get time to destroy them all before the white fireballs arrive.  

When Mundus sends the white fireballs, deflect them back to Mundus as described above. It's possible to deflect them in non-DT mode, but easier to do so in DT mode. To regain DT, quickly press L1 to cancel DT before the white fireballs hit Mundus - upon impact, you'll gain several runes of DT. Not only that, but there's enough recovery time afterwards to charge up a couple of Roundtrips or so :p 

And that's pretty much it for the long-range approach. To summarize: learn Mundus's telegraphs for his attacks and seek out attacking opportunities when you can. 

The short-range approach involves using the floating rocks - Air Hike is an immensely helpful ability to have here. Jump onto an "inner" floating rock in front of Mundus, DT, and mash away with the 3-Hit combo. On Normal mode, as long as you're in DT mode, you can probably get away with not even bothering to evade. On Hard mode, it's dicier. On DMD mode, it will lead to certain death.  

Nearly all of Mundus's attacks are harder to evade on the floating rocks, but there are a few which are just impossible to deal with: namely, any attack which results in the rocks being smashed (lava dragon, rock smash), the "one-by-one" spinning spheres formation, the white fireballs, and meteors-from-the-sky. For these, you should jump back down to the fixed platforms and deal with them from there.  

To summarize: the long-range approach is the "safe" one and the short-range approach is the "risky" one. Mundus is never that safe, no matter what you do, however.  

Once Mundus's lifebar is whittled down to 25%, the battle turns into chaos. Occasionally you will be lucky and get an unusually docile Mundus, but most of the time you will be running around like a maniac, evading meteors from the sky, lasers, etc. You should use both of the fixed platforms to give yourself more space for running about!  

Good luck! :p