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