Remark - game won't let you begin this mission until you don't destroy the Mobile Command Centre in the Rainier. Marker for this mission is in the alley in the northern part of the mentioned district.
When you begin the mission and listen to the conversation, start looking into the toilets on the marketplace. In each case you need to approach the toilet (they are all marked on the minimap) and move the finger right over the touchpad to open its door. Very probably that a bio-terrorist you're looking for is in one of the last toilets.
Start chasing a refugee, who'll be kidnapped by an angel after a while. Don't try to fire at the angel and chase him down. He'll run away no matter what you do, you can't prevent it to happen.
Return to the main part of the market and start exploring the four areas marked on the minimap. Focus on the part of this location where there are the remaining angels and the Akurans. Expect to be attacked by them. The good news is that the gangsters do not use powers and that angels disappear after a single hit. The bad news is that the blue rays that the angels shoot, deal quite a lot of damage. I strongly recommend that you remain in constant movement and hide behind covers, as soon as Delsin is severely wounded, in order to regenerate the health that you lose.
When the encounter ends, head for the construction site in the northern-east part of the Lantern District, nearby the bridge through which you get to the southern Seattle. Get onto the higher level of the site and then start climbing to get on the very top of the crane. Depending on your preferences, you can climb with Light Speed power or in a traditional way (grabbing the following interactive edges). When you are on the top, try to approach the second bio-terrorist, who'll also get caught by the angel.
As previously, you have no chances for catching up the angel whatever you do. Listen to what Reggie has to say and then head for the center of Rainier. Approach the toilets and when you see Reggie, listen what he tells about finding the angels' hideout.
When you regain full control, start running after Reggie dressed in the bio-terrorist suit. Plan consist on pursuit him, but you don't have to play to hard or use any particular powers. Just keep nearby the running away Reggie, who, after several dozens of seconds, will be caught by the angel. Just as it was planned.
During this final chase after the angel, paradoxically, you do not need to attach too much attention to that because, whenever the angel leaves you too much behind, the marker that signifies its position on the map will not disappear. Still, it is a good idea to use Light Speed to move around the area efficiently. Ignore simultaneously other angels you'll pass by, because attacking them won't give you anything. Chase ends next to the building in the southern-east part of the Waterfront and you have to use Delsin's power (again: best is Light Speed) to reach its roof.
After a short cut-scene, jump at the very bottom and begin the final battle of this mission. During this battle, you have, first of all, beware of angels again. Don't stop anywhere for a longer time and don't let them hit Delsin their strong distance attack too often. Besides, demons will appear there. Their attacks are also hurtful. Keep away from places on the ground, where you notice the red marks.
This battle cannot be won by eliminating angels and demons, as more will come at their place. Instead of that, focus on destroying those of nearby LED displays that work as portals (angels and demons come through them). To explode the displays you should use the best attacks of Delsin (Cinder Missile or Phosphor Beam). Don't forget also to regenerate health behind covers and picking up heavy ammo. Destroying all LED displays ends this mission and unlocks another one - Heaven's Hellfire.