The super-tough Iron Frog Mode unlocks after the fourth boss has been defeated. This is the hardest Achievement in the game and will likely be beyond some players' skill levels. You have to beat 10 super-tough levels in a row without dying. There is a serious element of luck, as power-up appearance and proximity can make all the difference between life and death - especially from level 6 and on.
When you do get a nice destructive power-up, try to use it to acquire another one and keep your chain of mass destruction going. Shoot through gaps whenever possible, and intentionally close gaps to rewind the line a bit.
I suggest doing this one after you've managed to get most or all Spirit Badges in Adventure mode, as you'll want your skills honed beforehand. Playing on a small screen to minimize the need for peripheral vision also helps.