You obtain a 'Great Recovery' bonus after being thrown/blown off of the stage and getting back on the stage quickly afterwards.
One of the easiest ways to get this bonus is after getting thrown off the stage by an enemy, start shooting your rockets against the nearest wall as you're falling to your death while being out of bounds, so you can propel yourself back on the stage.
It'll count towards your achievement progress once you see the 'Great Recovery' text pop up on the screen.
This achievement should come naturally as you play.