All creature and Hero cards can be upgraded or leveled up. Maximum level is currently at 20. Health and Damage, and sometimes DMP, will be upgraded when you level up.
To level up you need a card at the same lvl and type as the one you want to level up and you need Adaptorite. Adaptorite is earned while you play, both against AI in story/adventure mode and in PVP matches. Think of the crystals as XP.
You gain 1 adaptorite for loosing a game, and 2 adaptorite for winning a game.
To level up a card go to your collection and select the card you wish to level up. As mentioned you need Adaptorite (increases per level) and you need to sacrfice a card at same level and type as the one you are leveling up. It is here important to think who you want to keep. As when you are buying a card you sometimes get a card that does more or less damage or has more health or DMP as a similar card.