Not all races are equal. If one-on-one-only fight is considered: Mantis beats anything; Rockman beat anything but Mantis; Crystal is better than human or slug. Engi and Zoltan are weaker (but for different reasons).
Trained, experienced fighters are better than untrained. Kills, including room level kills while boarding give combat experience points.
(Cheaty hint (assume transporter and med bay): Lanius, Crystals and even Rockman (theoretically possible but increasingly hard for others) can turbo train continuously demolishing autoscouts and letting them repair)
Try to create numerical superiority, if at all possible, and avoid being outnumbered if you can, fight 2 vs 1 or in large room 4 vs 2, your crewmen who not have brawl partner but are in same room will shoot at enemy and help a little that way.
Rotate your crew. In 2 vs 1 situation often is enough to swap brawler and shooter roles once. Else, you can send crew away or to heal in med bay and replace with fresh.
Fight in operational and powered medbay. Engi medbot dispersal can help a little (but mostly is waste of a slot a little).
Antiboarding drone is far from efficient investment mostly, but valid choice in situations with small Engi or Zoltan only crew.
Upgrade (and/or man) the doors. Open doors for them to let them where you want.
Suffocate enemies by venting rooms they in or most of the ship You can jump around with only few rooms actually having air at all (helps also against fire a lot).
Do crazy things, like drop fire bomb in your own, subsystem-less room. That's rarely sane, but can save you once per year.
Post edited December 24, 2016 by Enneagon