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.
If you want to full fil your Moga HP, The only thing you can do is rest them. Isn't it? But, I discover new way to full fil your Hp. You just need to go back to your home and then refresh the page. After that, you found you start from Home and your Moga is in the full HP. I hope this can help all of you.