Arcade level 1 on easy. Set the lives to 3 (minimum)
1. Start the game and press start on the 2nd controller and spawn the 2nd player, 1 bomb appears, collect it.
2. Play normally through the level, but just let 2nd controller idle and die until the 3 lives run out. When you spawn again with the 2nd controller, another bomb appears, grab it.
3. The last transport helicopter near the end always drops an extra bomb after you destroy it, grab it, now you have 6 and are ready to face the boss.
4. When the boss battle begins, spam bombs from the 2nd controller to keep yourself alive more easily, but you should be able to do it by just playing normally, the boss shoots only a few bullets on easy and dies pretty fast. Once the level ends and you have 6 bombs when the boss dies, you will get the achievement after the level.