Here is the full list of all 37 Phantom Jump achievements.
Defeat the Sunrise Mountains Boss
Defeat the Morning Meadows Boss
Reach 112% completion in Sunrise Mountains
Reach 112% completion in Morning Meadows
Reach 112% completion in Shaded Grove
Reach 112% completion in Flooded Caverns
Finish all standard Sunrise Mountains levels without dying
Finish all standard Morning Meadows levels without dying
Finish all standard Shaded Grove levels without dying
Finish all standard Flooded Caverns levels without dying
Get 30 perfect Phantom Jumps in a row
Finish all standard Midnight Peaks levels without dying
Vanquish the Shaded Grove boss
Reach 112% completion in Moonlit Peaks
Get maximum percent completion in every world
Escape the Flooded Caverns
Keep the alien from overtaking earth
Win an online game
Complete any speedrun
Beat Phantom Jump for the first time
Perfectly time a Phantom Jump
Get an 'S' rank on every level in Sunrise Mountains
Get an 'S' rank time on every level in Morning Meadows
Get an 'S' rank in every level on Shaded Grove
Get an 'S' rank time on every level in Flooded Caverns
Get an 'S' rank on every level in Moonlit Peaks
Reach 100% completion in the Bonus World
Get an 'S' rank on every level in the Bonus World
Finish the Bonus World without dying
Reach 100% completion in Sunrise Trailhead
Get an 'S' rank time on every level in Sunrise Trailhead
Finish all Sunrise Trailhead levels without dying
Don't follow the directions on the tutorial
Get an 'S' rank on every level, even the secret ones
Grab a pickup and complete the level
Find every pickup in Phantom Jump
Get every achievement