Here is the full list of all 35 Backpack Hero achievements.
Carry at least 5 arrows
Win a Quick Run as CR-8
Win a Quick Run as Tote
Win a Quick Run as Pochette
Carry at least 4 cursed items
Win a Quick Run as Satchel
Carry a helmet, clothing, two gloves, and footwear
Win a Quick Run
Win a Quick Run as Purse
Win a Run in Hardmode
Defeat Disorder
Give a Tasty Fly to a merchant
Stack at least 50 poison
Discover at least 700 items
Unlock Pochette
Discover the Frozen Heart
Discover the Magma Core
Unlock CR-8
Discover at least 400 items
Unlock Tote
Carry at least 5 manastones
Have at least 5 status effects at the same time
Discover the Enchanted Swamp
Unlock Satchel
Survive the Raid
Carry at least 7 consumables
Unlock the Town Hall
Discover the Bramble
Wear a shoehat on your head and one on your feet at the same time
Discover at least 200 items
Carry at least 5 shivs
Attract at least 40 residents to Haversack Hill
Discover the Deep Caves
Carry at least 5 structures
Find Prada's Locket