Raiden IV: OverKill

For whatever reason these two achievements are reversed. Waiting a boss out unlocks Fireworks and setting off 7 bombs unlocks Perseverance.

Other than that these achievements are pretty self-explanatory. For an easier time with Perseverance you can set your starting bomb count to 6 in the settings than collect one more. One of the towers in level 1-1 has one inside.