2nd encounter, equip shotgun.
Use DT with the shotgun to have a great spead of bullets, this'll help with destroying those annoying laser firing orbs. This makes this part soooo much easier, I found.
Just remember to not use up all your DT, save some for his summoned lava dragon, you get a green orb out of it and this is one of those battles where you need as much help as you can get. Boss battles don't come harder than this in the original DMC.
By now you should have purchased all purple orbs, all available blue orbs should have been bought and you should have found a lot of the other ones in secret missions or just randomly lying about.
Use DT with the shotgun to have a great spead of bullets, this'll help with destroying those annoying laser firing orbs. This makes this part soooo much easier, I found.

Just remember to not use up all your DT, save some for his summoned lava dragon, you get a green orb out of it and this is one of those battles where you need as much help as you can get. Boss battles don't come harder than this in the original DMC.
By now you should have purchased all purple orbs, all available blue orbs should have been bought and you should have found a lot of the other ones in secret missions or just randomly lying about.