Here is the full list of all 20 Armed with Wings: Rearmed achievements.
Reach a Double Flag Post
Collect 500 Orbs
Get a x25 Combo
Get a x10 Combo
Collect 100 Orbs
Reach a Single Flag Post
Collect 1000 Orbs
Get a x50 Combo
Complete the Story in Futile Difficulty
Complete the Story with Vandheer Lorde
Complete the Story with the Katana
Complete the Story with the Katana on Futile
Collect all Relics
Complete Level 40 without being Revived
Unlock all Equipment
Reach Wave 5 in Survival
Reach Wave 10 in Survival
Reach Wave 20 in Survival
Reach a Triple Flag Post
Complete the Story in 60 minutes or less