I'm going to write just a quick guide to list a few hints per mission based on the differences. I did not find Domino to be that useful, but Darkvision worked fine and Blink worked as well as it always has.
Mission 1
This one is going to be the same since you did not have powers yet at this point.
Mission 2
You cannot use the rat hole trick to get into the tattoo parlor, but there is a door in a back alley if you go through the fence on the right. You should use the pipes above to avoid the hounds. The best way into Shan's house is by using the secret knock, which means you really don't need the tattoo unless you are doing contracts. Robbing the Black Market in this mission requires original powers, so you cannot do it.
Mission 3
You cannot get the Poppy Tincture in the auction unless you are prepared to fight everyone in that area. You can rob the Black Market and get it for free, no powers required.
Mission 4
The main thing here is that you cannot trace paths of enemies and there are a lot of them. The other thing is that if you didn't get an achievement for doing Semblance on a certain person you can't get that one with these powers. Robbing the Black Market in this mission requires original powers, so you cannot do it. Before you end the mission, make sure you get all of the grenade and mine upgrades that you can. They come in very handy in the next mission.
Mission 5
You will find grenades to be very useful since many enemies come in groups. The mines are also very useful. You can cut out a lot of the risk past the overturned rail car that you crawl through by tossing a grenade at the group that is gathered there. You will have to wait until the creature disappears, however, before you poke your head out. If you go to the right at that point it takes you to a catwalk that gives you a great vantage point for sniping enemies below or blowing them up. The moment you touch the eye, beware of an enemy coming to investigate. He won't do it on a reload, only the first time you enter the Void. Once you get the goal to go to the place where the Outsider is, you can run there and not worry about enemies because you exit into a new area the moment you reach the goal.