Ratchet begins the game with 10 hit points. As he defeats enemies his experience bar will move (located directly underneath his hit points). Every time he "levels up" this bar will reset and he will gain an additional 10 hit points. During your first playthrough you can only get Ratchet's health to 100. You must enter Challenge Mode in your second playthrough to continue all the way up to 200.
You can view Ratchet's current and maximum health by pressing and holding
. The trophy will unlock immediately after that final "level up" to 200 health.