Here is the full list of all 41 I Hate Running Backwards trophies - there are 26 bronze, 10 silver, 4 gold and 1 platinum.
Collect every powerup in one run
Destroy a weapon crate
Die
Collect all trophies
Deflect 20 rockets
Kill Scrapjack using only the hammer
Kill King Scorpion
Kill the Biomechanoid without being hit
Kill Scrapjack
Kill Biomechanoid
Finish a loop with all 6 curses active
Heal for 20 health during one session
Destroy 50 watchtowers
Use ultimate ability 5 times in the same run
Deflect 500 projectiles
Detonate 50 Explosive traps
Kill 1000 enemies with a hammer
Gather 5k Mojo from destruction
Finish a game loop
Kill the werebull
Kill Ugh Zan without taking any damage
Finish a loop without receiving damage
Kill King Scorpion before he burrows
Get the combo counter to x50
Knockback 100 enemies
Deflect 50 cannonballs
Kill 10 RoadBulls on the Road ground
Kill the Lava golem
Destroy 30 mines while invulnerable
Gather 50k chunks from destruction
Kill the second form of Ugh Zan
Get to King Scorpion using only the hammer
Freeze 100 enemies
Kill Ugh Zhan
Unlock 15 special weapons
Destroy a secret trash container
Kill Biomechanoid while four curses are active
Destroy a special crystal in Crystal cave
Kill King Scorpion while two curses are active
Collect 666 souls
Finish a loop without receiving damage with 6 curses active