This mission is basically a boss fight between you and an angel known as He Who Dwells. Luckily, you'll have plenty of smoke and neon sources around the area to help you. It's recommended that you have unlocked the Laser Focus ability, and plus, the Phosphor Beam will also come in handy here.
Use the video beam to reach a higher platform, and from there, you'll start to fight the angel. He Who Dwells will summon smaller angels around him, all of which takes a single hit to defeat, but this also means you cannot hurt He Who Dwells, not until his angel minions are out of the picture.
This large angel can do a lot of damage to you. Therefore, it's recommended that instead of standing exposed on the platforms, try to bounce some shots at the angel from hanging off the ledge. This is effective since you'll be able to hit him, while he won't be able to hit you. Of course, just make you don't have any obscuring obstacles in your way.
After the angel takes several hits, the platforms will sink and the fight will move to the other side of the arena. Use the video beams to cross the hot lava and resume the fight. Continue utilizing the method mentioned above, and once the angel is down, you'll then be faced with a karmic decision — either redeem Eugene (Good Karma) or capture him (Evil Karma). After making your decision, the mission ends.