Boss Attacks

As Nightmare 1's, except: 

Boomerang - A metal 'arm' detaches itself from Nightmare's side and unfolds into a boomerang. It rises, hovers for a couple of seconds, then begins spinning at a rapid speed at around the arena. Once it has spun around several times, it returns to Nightmare. While it's spinning, the top core is exposed, but it's extremely dangerous to try and attack whilst the boomerang is spinning. The boomerang can be parried, however.

The safest time to try is when it first emerges - stand underneath it, then, before it starts spinning, do a Rolling-Blazed jump straight up or a rising High Time. If the parry is successful, the boomerang will retract into Nightmare and you can attack the top core unhindered. If you miss that opportunity, the boomerang can be parried with RB or a slash as it's spinning around the arena. Otherwise, just go to the edge of the arena and wait until this attack is over. 

Underworld: 

This is the same as the Underworld in the Nightmare 1 fight, except that you get Griffon as a Shadow boss this time. Shadow Griffon may only basically have two attacks - the V-Bolts and the Horizontal Bolts - but he's surprisingly tricky to deal with. At any rate, the V-Bolts are easily evaded by hopping over the side of them, but the Horizontal Bolts are tougher - your best bet is to stand still, then alternate between jumping over the low bolts and letting the high ones pass over your head. Since Griffon's bolts come out rather fast, you should concentrate on avoiding them, then charging up a Meteor or Roundtrip after the attack is over and hitting Griffon on the counterattack. You can also go for a short-range knockdown strategy, as outlined in the Griffon 1 and 3 battles. Use plenty of grenades or E&I, too. 

Nightmare 2's Patterns/Mechanics: 

The majority of this was covered in the Nightmare 1 section, but there are a couple of new things to know for Nightmare 2.  

Firstly, the attack pattern has become slightly more complex than before. It now goes like this: 

[Beginning of Battle/After Return from Underworld] > Ice Beam/Guided Missiles > Triple Stab > Ice Beam/Guided Missiles > Triple Stab > Boomerang > Triple Stab > repeat  

Note the 1 Boomerang for every 2 Ice Beam attacks? Also, the Boomerang attack cannot be substituted for any other attack in the way that the Ice Beam/Guided Missiles can - if it's the Boomerang's turn, it will come out regardless of what you do. 

Secondly, Nightmare's cores can be turned red for the first time. To be honest, on Normal/Hard mode I reckon it doesn't  make any significant difference if you turn them red or not - but on DMD mode, it does actually do so. You will feel the pain less against DMD Nightmare 3 if his cores are blue or green, instead of red. 

If Nightmare's cores were turned green in the previous fight, they will be green at the beginning of the Nightmare 2 fight - changes in core colour carry over to the next Nightmare fight. 

The Battle

Nearly everything written about the Nightmare 1 battle is applicable to this battle. On the whole, this is definitely a better arena for fighting Nightmare in, but you still get the jarring camera angle changes. To avoid them, you should only run down that side of Nightmare which is facing the grate the Philosopher's Egg is in. It sounds restricting, and it probably is, but it works. The camera is pretty good down that side - you get an almost top-down view of Nightmare.  

Otherwise, I don't really have anything to say which I wouldn't refer you to the Nightmare 1 section for. If you do want to avoid turning the cores red, then you should use only charged PPKK combos or Meteors in this fight.  

It's possible to avoid the Boomerang attack altogether by strategically planning your visit to the Underworld. If you go after two Ice Beams and two Triple Stabs, the attack pattern will be reset upon your return from the Underworld, and Nightmare will once again do two Ice Beams and two Triple Stabs before doing a Boomerang attack - that should give you more than enough time to defeat him. Even on DMD mode, that will give you enough time to defeat him, but only if you succeed in parrying the Triple Stab attacks.