Here is the full list of all 20 Mantle achievements.
Finish the Cave Levels
Finish the Wind Levels
Finish the Fire Levels
Complete the End Levels
Complete the Cave levels with less than 5 deaths
Complete the Wind levels with less than 5 deaths
Complete the Fire levels with less than 5 deaths
Complete the End levels with less than 5 deaths
Complete the Cave levels in under 5 minutes
Complete the Wind levels in under 5 minutes
Complete the Fire levels in under 5 minutes
Complete the End levels in under 5 minutes
Navigate the darkness
Teleport offscreen to your death
Teleport directly onto spikes
Teleport directly into lava
Teleport 5 times without touching the ground
Open a locked door
Survive rising lava
After falling from a long height, land on spikes.