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