Here is the full list of all 40 I Hate Running Backwards achievements.
Finish a loop with all six curses active
Finish a loop without receiving damage
Deflect 50 cannonballs
Kill Ugh Zan without taking any damage
Finish a game loop
Kill the second form of Ugh Zhan boss
Kill Ugh Zan boss
Kill Biomechanoid while four curses are active
Kill the biomechanoid without being hit
Knockback 100 enemies
Destroy a special crystal in the Crystal cave
Destroy 30 mines while invulnerable
Deflect 500 projectiles
Kill Biomechanoid boss
Heal for 20 health during one session
Freeze 100 enemies
Kill the Lava Golem boss
Use ultimate ability 5 times in the same run
Kill 1000 enemies with a hammer
Kill the werebull
Kill the Scorpion King before he burrows
Unlock 15 special weapons
Gather 50k chunks from destruction
Kill Scrapjack using only the hammer
Detonate 50 explosive traps
Destroy a secret trash container
Kill Scorpion King while two curses are active
Destroy 50 watchtowers
Get to the Scorpion king using only the hammer
Kill 10 RoadBulls on the Road ground
Kill Scrapjack boss
Gather 5k chunks from destruction
Kill the Scorpion King boss
Get the combo counter to x50
Deflect 20 rockets
Die
Collect every powerup in one run
Destroy weapon crate
Collect 666 souls
Finish a loop without receiving damage with all six curses active