What strategy do you need for Chess mode? Try to get the power squares? Beat the opposing teams leader before they beat yours? If you're having trouble with something as basic as Chess Kombat, perhaps you should go back to pong.

Basically you just need to occupy the green power cell blocks and keep your characters there. If you're not that good at kombat yet then put it on a lower difficulty setting until you get the hang of it. Plus I found it helps me personally when you do most of the attacking. You keep the opponents from getting any power. I play chess on max difficulty and I also find that you should destroy the sorcerers as soon as you can so then they can't cast any spells.
As for puzzle kombat, always try to gain a bomb bonus in the begining of each match. This helps a lot with your super bar. Also if you're a beginner, then you should pick someone with a super move that is beneficial to you (i.e. Kabal's double bomb or Ermac's levitate) so then you'll have a better chance at winning. Also try your hardest to get combos. It helps you out so much in the end.