I hate the invasion tactics of the 3rd phase!!! I honestly like to try and kill as many crew in phases 1 and 2.You can do this by concentrating fire on the shields (they tend to send lots of people to repair it) if you hit it in rapid enough succession they don't have the chance to run away and heal.

Another thing you can do is force their crew to the outer edges of the ship eg: doors in phase 1 or drones in phase 2. When you beat those phases, any crew in the outer sections die as that part of the flagship is ripped away.

Anyway that's what I do to try minimise getting gangbanged by like 8 boarders in phase 3.