For this achievement all you need to do is stay alive for 30 seconds in a boss battle without shooting. I would recommend doing it on the first level boss, if you go into the battle with full health you only need to avoid one of his attacks and you will have enough health to survive the rest of his attacks for 30 seconds. You can move and jump for the achievement and it will pop during the battle so you will know when you have completed it also you don't have to beat the boss you only have to survive that 30 seconds
If you would like a video guide for the whole achievement I have included my guide below.