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