Boarders and Sun jumps

[BluntInstrument]

I agree with the others who said level 2 doors are a necessity. If you're at a sun, you should have sensors up. Therefore you can use your upgraded doors and airlocks to "herd" the mantis's to the med bay, at which point they'll be almost dead and easy pickings. Just empty the oxygen from the room the mantis's tele into, and from the surrounding rooms that want to discourage them from using. Let them beat on the door you want to them to go in for a bit, and then open it at the last second so you retain control over it.

Frequently, it's possible to herd them in a way that allows you to keep crew at your engine and helm. Then you jump away quickly if end up going south.