When you reach QuAsSy after fulfilling all the other requirements of Slash's quest; he will be there looking defeated. In order to help him, you have to recycle yourself which is an option exclusive to this scenario. Once you do so, you will be reduced to one heart of health and so you should recycle other parts to regain some health. You then have to hit QuAsSy once to trigger the good ending of the game and get the achievement. If you are quick enough, however, after recycling yourself; you can hit QuAsSy without having to deal with any lasers or enemies. Getting this achievement also unlocks Slash as a playable character.