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