You fight an angel summoned by Eugene during the eleventh mission of the game: Heaven's Hellfire. Encounter begins when you get to the cellar and search it a bit.
At first, several words about this encounter in general. It's divided onto several parts, where your primary task is to get rid of huge amount of angel's health and avoid all his attacks and other dangers. The last category is lava, filling the whole arena. Falling into lava doesn't mean you're dead, but you have to hurry onto the dry land. In such a case, changing into smoke or Light Speed power will be useful.
Another important thing is moving around the arena. You should, in majority, rely on energy pillars like the one shown on the screen above. Getting into the energy torrent will jump out Delsin. For getting onto shelves safely, you should also use the option of floating. Use this skill when you want to get closer to the boss and fire at him while remaining mobile.
At the beginning, boss will have only one attack - a strong beam of energy fired at Delsin. Stay mobile and jump between shelves and wait for angel to finish his current attack. I don't recommend hiding behind pillars, as they'd be destroyed. You can try to grab the outer edges of shelves, on which you should remain safe.
You can use both Smoke and Neon powers to attack angel. There are nearby points to regenerate energy used for offensive powers. One of them is shown on the screen above. Use those points mostly to replenish Heavy Ammo.
As you probably figure out, the best attacks you use with R1 button are the best one to decrease angel's health bar. I recommend to mostly use them and the standard distance attacks (R2 button) between the first ones.
First part of the encounter ends after several successful hits. After that, you're again in the cellar. Approach the TV you see to get to the second stage of the battle.
Second part of the encounter brings two important changes. First, is a boss attack, Besides firing an energy beam, he'll also fire explosive missiles at Delsin from time to time. When you see angel preparing to this attack, jump onto other shelves to avoid damage. Attack angel the same way you did previously, using the strongest abilities (R1 button).
The other new thing is the boss moving around. When only you notice that he changes into a group of angels, fire at them to lower the boss' health bar. The more important is what will happen in a moment. The part of shelves will lower. You have to act quick to not get into the lava. You should start floating in the air and reach one of the shelves with the vertical pillar of light. After landing, use the mentioned "elevator" to get onto the new arena and resume the boss fight.
Continue attacking from distance, remember to keep Delsin alive (start jumping around when heavily wounded) and run away from platforms falling into lava. You return to the cellar when boss' health drops below the half. Get to the another part of the building to move to the third stage of the battle.
In this part, the only new thing is that boss will be supported by the smaller angels (screen above). ALWAYS focus on eliminating them firstly, because until that, the main boss will be immortal. The rest of the encounter has no more changes, so you have to beware of two types of boss' attacks and platforms falling in lava.
Decrease the boss' health bar and try to keep Delsin alive. Encounter ends when health bar is down to zero.