For a summary:
1) Play cards with high card strength level, but low ability level
2) Make your training specialised, rather than generalised. (for instance, Mai the Sumo wrestler should focus on striking and grappling)
3) Use your glass cannons first to get a head start when choosing the order of your lineup.
4) Use guard or evade if you suspect you might not win the card round.
5) Invest in cards with status effects.