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