How to beat Riku IV:
The Key: Put as many Zero cards as you can at the very front of your deck. Seven of them at the very least. Then put six or seven cure cards right after the zeros. Make sure your cure cards are sevens, eights, nines, or zeros.
Don't attack him in the beginning. Concentrate on only breaking his sleights (Dark Aura, etc.) with your zero cards, healing with your cures when you need to and avoiding his other attacks. Then once he is running out of cards and reloading quite a bit, that's when you open the can of whoop @ss.
Of course try to have as many high level attack cards as you can, a high level Cloud and Tinkerbell card are nice to have too as is a Mega-Ether or Mega-Potion. Put Oogie Boogie and Vexen in your deck too, however if you follow the KEY above you probably wouldn't have to use them.
How to beat Axel II:
The exact same way.