the one hit kill seems to bug out and you don't get achivements.
I am not sure about the first but in regards to the achievements issue, from what I have seen at Steam's forum for this game it's most likely not the trainer. In fact, it seems to be happening to almost everyone regardless of using a trainer or not. Seems that the flagging/tracking of the achievements is bugged currently...
Though, it seems restarting the Steam client before starting the game has fixed it for the most part. Anyway, it seems to have helped on my end at least.
The trainer seems to affect the boss robots in the tower making them have unlimited health at least on my game it does.You can't have the trainer running aganst those boss robots gotta beat them honestly.