To unlock this achievement you need to complete the challenge and its extras in Perpetua.
Challenge (purple platform)
* Perpetua: Hit as many checkpoints as you can!
Extras (purple platform)
* Ridiculous Speed: In Perpetua hit 500#.
* Ludicrous Speed: In Perpetua hit 750#.
* Sonic Boom: In Perpetua hit 1225#.
* Getting Started: In Perpetua hit 5 checkpoints.
* Locked On: In Perpetua hit 15 checkpoints.
* Stay On Target: In Perpetua hit 25 checkpoints.
* Rime of the Mariner: In Perpetua hit 10 checkpoints using the Albatross Wings.
I suggest you do this challenge with the Albatross Wings so you complete the Rime of the Mariner. You'll pick up some of the other extras too with those wings.
The Albatross Wings can be found in Spiral Heights: Fly through the tunnel. The tunnel is located on top next to the waterfall on the right side of it. Fly all the way through the tunnel and follow the cavern bridge to the village in the back corner; these wings can be found sitting near this village.
If you don't succeed completely with the Albatross wings, switch to the Energy Wings as those are much more maneuverable.
The Energy Wings can be found on the highest point in Magma Core.
Tip: You can switch between tilt and touch controls with the button on the right side of the screen.