Instructions
Locate a bed anywhere on the game map. Beds are most often found in towns, but occasionally resting spots are on the map.
Press the "X" button once you approach the bed to bring up the sleep time menu. Sleeping serves two purposes. The rest heals any wounds you may have and also makes any repairs needed to your Mister Gutsy.
Scroll the time dial to determine how much time you want to rest and press the "X" button. The amount of time is irrelevant to healing your character and Mister Gutsy.
Check the companion wheel in your inventory by pressing the "O" button. Any damage Mister Gutsy has taken during the course of your journey should be healed. This technique will work for any companion you pick up along the way.