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