This is a fun puzzle that contains all the moves available on the curvy-copter. I forget which. In any case, interestingly, I don't reduce it to a curvy-copter as you'll see in the steps below.
There are 3 types of faces: large pedal, small pedal, and diamond. (Should be reasonably clear which I mean here.) And there is just one type of edge piece. There are only two types of rotations: corner and edge. (The faces don't turn.)
Solve the diamonds first. This is a trivial matter of turning the edges.
Solve the edges next. There is a trivial tri-cycle for this. It's a commutator between an edge and corner. If the edges won't solve, turn a single corner once, and then continue tri-cycling.
Solve the large pedals. This is a trivial tri-cycle (or commutator) between adjacent edges. Use corner and edge turns as setups.
Solve the small pedals. This is the trickiest part. My stratagy was to perform the tri-cycle in Step 3, but with a trivial setup to ensure that all 3 large pedals involved are the same color. This will tri-cycle 3 small pedals while leaving the rest of the cube invarient. You then have to find setups for this stratagy to tri-cycle the desired triples of small pedals. Where it gets tricky is in realizing that sometimes you have to change orbits in the setup sequence. Doing so requires a special move only available on the curvy-copter, which is a sub-group (or factor group?) of this cube.