We got the Prima Games strategy guide which was superb in that explained every single mechanic of the game.
After reading it my brother worked out how and then made a super bad ass psy team.
The key understanding is that there is a base psy attribute for characters which can never change and then another one which can improve through experience.
So your previously best characters probably land up having terrible base psy stat, so you need to abandon them ultimately unfortunately.
So he made lots of psy labs to find the strong soldiers. Then started getting them to skill up psy skill on missions.
Once they could mind control then it was to skill them up in other regards like accuracy and reactions. You would mind control aliens, have them drop their weapons then end your turn with them facing away from your guys ready to shoot them. During the aliens turn they would start walking and then get shot by the reacting “rookie” 3 blocks away. The rookies accuracy and reaction improved quickly.
If I recall he managed to complete the final mission in like 3 turns per part by mind controlling the first alien he could see, then using that to find the next alien to mind control and so on.