The highest level is 10.Damn, those are some high levels. My highest level is 8, and I've already completed the entire game. Is level 9 the highest a mon can get?
Level 1 and 2 grant +3 damage each, then after that it's +2 per level for a total of +20 from the base attack power.
(Edit: Thing is, after level 5, the EXP gain gets drastically reduced, so usually grinding to level 5 is enough.)