Gunkid 99 (JP)

Zero-Baggage is an ability type perk you can buy form the in-game shop with coins earned during a level. Simply buy it, equip it in your loadout on the main menu and finish a level with a bigger score than you previously set to unlock this achievement. Be warned, this game is very difficult at the best of times so it's advised to go for this achievement early on. You will have to finish each level at least once with the basic score requirement met, before redoing them all to gain an even higher score to unlock the next world, when redoing a level, that's when to attempt this.