This page in our guide to Control contains a description of the battle with one of the bosses, esseJ. Defeat this boss to get a trophy/achievement of the same name.
Where to find the boss?: During Self-reflection side quest.
Description: esseJ is your reflection waiting on the other side of the mirror. The enemy has a very similar assortment of attacks to yours and the fight is divided into several phases. In the beginning, esseJ fights on the ground and will shoot missiles at you. However, the boss isn't as mobile - you should be able to deplete her health fast by catching the rockets and throwing them back at the boss.
The second phase is very similar to the first - the boss starts using telekinesis and, for example, covers. As before, try to quickly deal as much damage to the boss as possible - you shouldn't have problems with that. The third phase is the most challenging - esseJ flies up and attacks you from the air.
The boss can avoid throws with ease so remember to also use your firearms. If you need to restore health, you can do that by using items lying on the ground after damaging the boss. There aren't many covers in the room, so the best move would be to use the Shield and try to finish the duel as soon as possible - time can work against you, so it is worth risking a few attacks that could potentially take a lot of the boss's health.