The Battle
On Normal and probably Hard mode, you can get away with abusing Air Raid like crazy - unlike in the Griffon 1 battle, using Air Raid won't incur any horrible camera angle changes. Use your guns whenever you can to restore DT. (Annoyingly enough, shooting at the hologram wing doesn't restore DT - another reason to hate it.)
Otherwise, Griffon 2 is almost inaccessible in this fight. There's no easy way of fighting him - except one :p
Griffon isn't the brightest bird in the aviary, hence there's a fairly straightforward loop you can get him into - the divebomb loop. Once Griffon divebombs the deck for the first time, he will continue to divebomb it over and over - not forever, but for a long time. You get loads of time to attack him while he is on deck. He is a sitting duck, literally.
Incidentally, you can get Griffon to land on either the lower or the upper deck, but not the middle one. I only get Griffon to land on the upper deck if I want to use the "E&I-from-the-mast" strategy - something I'll outline a bit later on.
No matter what you do, Griffon will sooner or later eventually divebomb whichever deck you're standing on. However, you can force him to land much earlier than he would otherwise by refraining from attacking him (at all) and camping out on the right hand side (from the player's POV) of the lower deck. Griffon will send out a minimum of two energy wings. If you haven't damaged him, these should be "weak" wings and hence easily destroyable in mid-air with a few E&I shots. After two (or possibly more) energy wings, watch for Griffon swinging in above deck. When he rises into the air, out of sight, and shrieks, that's your cue to jump away as he descends - jump towards the right hand side of the ship (again, from the player's POV).
After Griffon lands, he will charge up his electricity bolts and the screen will darken. You can attack him with anything you like during this period: DTed sword combos, Air Raid, etc. However, the single most damaging attack you can do is a fully-charged Meteor Lvl 2 - just two of these, if they hit for maximum damage, will defeat Normal/Hard Griffon outright.
The good news is that you can fit in two fully-charged Meteor 2s before the bolts come out ;p
To get the most damage from Meteor 2, incidentally, make sure you're standing right in front of Griffon (or right behind him) and not off to the side of him.
Once the bolts come out, then you should get a certain distance away from Griffon. You don't need to go very far, just enough to distinguish the homing bolts from the general bolts which surround Griffon. Roll or jump to evade the first homing bolt, then stand still to let the second one pass. While the electrocution attack is going on, you can fire E&I or taunt to regain DT in between pairs of bolts.
When the electrocution attack is over, you get yet another opportunity to attack Griffon as the screen lightens - there's enough time to fully-charge up one Meteor Lvl 2, for example.
To make certain that Griffon divebombs the deck again, remain on the lower deck by the raised cylindrical platform. As long as you don't go away, Griffon will invariably do another divebomb attack straight away.
There is a more specialist version of the divebomb loop that you can use, which has certain advantages if you can master it. It involves Air-Hiking up to the top of the mast, and firing at Griffon for extra-damage from a certain "sweet" spot. You'll need to get Griffon to land on the upper deck first of all - the moment he shrieks, or even a second or two earlier, Air Hike over to the square platform on the mast on the middle deck. Air Hike up to the crow's nest at the top (Dante will magically pass through the platforms), then go to the right hand beam.
The "sweet" spot is variable, unfortunately. Some players stand a third of the way along the beam from the left, but I usually just go the end, which is infallible, at least for me. If you get the right spot, you can fire DTed E&I at Griffon for humungous damage - on Normal/Hard modes, you should defeat Griffon in one go upon the beam if DT lasts. On DMD mode, it will take rather more than that, and you'll have to Air Hike back down to the upper deck once or twice in order to trigger Griffon into doing his divebomb attack again.
The advantages of this strategy are that a) you don't need to worry about the electrocution attack and b) you don't need to worry about Griffon's parting bolts upon defeat - just jump straight down from the mast and the parting bolts will bypass you.
If you use another strategy, then you can use Vortex Lvl 2 to get through the bolting parts safely - but don't let go of the attack button! Otherwise, it's a bit random, but if you run to the other side of the ship they're normally evadeable.