The best way to level up in Monster Galaxy is to pick a Moga with a strong attack, such as Gryph, Messi or Tigon. You should aim to fight Mogas that are a couple of levels above your own, then choose the weakest Zodiac sign Moga of the enemy. Continue to attack and you will level up - the fastest way is to battle Mogas a long way above your own level, though difficult, and use plenty of bonus attacks.