Alastor is the boss of Chapter 2. The fight will take place of a multi-tiered tower located in some abandoned part of purgatory. There are 4 phases to this boss fight, which don't actually change that much.
Phase 1: Alastor will fly at you attempting to swipe you while brimstone falls from the sky. I would personally use the chain-gun against him and keep bunny-hopping to avoid the brimstone and from Alastor. He lets you know he is coming by a large screech, so you know when he's close. Once his health is depleted he will smash through the floor.
Phase 2: This time he will spit fire at you and attempt to get close enough to claw at you. Keep running around in circles firing your chain-gun and rocket launcher at him to defeat him. There is ammo located around the edge of the map.
Phase 3: Exactly the same as Phase two.
Phase 4: This is the final phase. He will copy his technique from Phase 2 and 3, the only difference being that when his health is depleted he will use statutes located around the edge of the map to heal himself. You can't destroy these statues unless he is healing himself. So deplete his health and then fire at the statues. They break after one shot, so I would recommend using the Chain-gun again and simply spraying at the statues in a line. Once all the statues have been destroyed, empty his health bar again to beat him once and for all. In-case you run out of ammo, there are always ammo packs located around the rims of the map.
If you're attempting this on Trauma and need some advice for which tarot cards to use, I would recommend the 4X damage and the 2X as well as the silver card that allows you to use the Gold cards 3 times. This will make short work of Alastor and easily allow you to beat him within the 5 minute mark. It is possible without the cards, but obviously these make it considerably easier.