You learn the repair skill midway through the first stage. If you hit RB, the skill enables you to regain life.
To get this achievement, simply never hit RB until you finish the game with one of the characters. You can die as much as you want and retry within the stage, just never hit RB.
If you do happen to accidentally hit RB, you can simply replay the stage to get it to count. I accidentally healed myself during Stage 3, then went on to beat the game as Ares not healing myself on any other stage. Once I finished the game, I replayed Stage 3 and beat it without healing myself. After beating the boss, the achievement popped.