You need to complete all goals, challenge and extras in Sporelle. Sporelle is unlocked after you find all the blue crystals. Those are scattered all over the world.
Sun Flare: Collect a Sun Flare Crystal after it has been released from the mushroom stalk at the surface of Sporelle. Complete Room to Grow Challenge to grow the mushroom.
Spectral Lens: Find a Spectral Lens in Sporelle. It needs to be placed on a spectral mounting pole.
Ethereal Harmonic: Collect this Dimensional Relic in Sporelle. Chaotic ethereal auras will cause instability in the dimensional signature pattern. An Ethereal Harmonic will smooth the celestial imprint.
Sporelle (Red platform): Use the red platforms to explore the lower reaches of Sporelle. Goal time 1:20:0.
Tunnels (Green platform): Descend through the tunnels of Sporelle and land on the green platform. Goal time 1:10:0.
Full Circuit (Blue platform): Take a full tour of all three shafts in Sporelle then land on the blue platform. Goal time 1:35:0.
Room to Grow (Purple platform): Carry spores to the dead mushroom stalk on the surface of Sporelle to regrow a mushroom. use the purple platform to start. Goal time 2:20:0.
Bubbles Blowing (White spinning platform): Who turned on the Sporelle bubble field generator? Collect as many bubbles as you can!
Sporelle Landing: Land on the gold platform in Sporelle.
Dark Tunnel: Find the dark tunnel hidden at the bottom of the Sporelle pits!
Sun Flare: Finish the Room to Grow (purple platform) challenge. You don't need to beat the challenge in the alloted time to unlock the Sun Flare. Pick up the Green crystals and fly out of the pit to the broken mushroom. Repeat to more times. I suggest wings with great power like the Quetzal Wings and the Energy Wings. To beat the challenge within time limit I used a fully charged Phoenix Wings.
Spectral Lens: Start at the gold platform and it is directly below you on a rock at the bottom of the pit.
Ethereal Harmonic: Fly into the pits and fly through the tunnel from the Squeebil village.
I used the Phoenix Wings for all challenges. I made sure I have 5 boosts before I started the challenges.
The Phoenix Wings can be found in the cave behind the Fiery Gates in Magma Core. Finish the Gathering The Flock Challenge in Oasis (Purple platform) to obtain the key.
Tip: You can switch between Tilt and Touch controls by pressing the button on the right side of the screen.