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