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