Here is the full list of all 51 No More Heroes: Heroes' Paradise trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
Obtained all Trophies
Used whatever means available to beat 5100 regular enemies
Completed the game on "BITTER" difficulty
Obtained a total score of 15,000,000 points in Score Attack
Obtained a total score of 10,000,000 points in Score Attack
Obtained a total score of 5,000,000 points in Score Attack
Collected all Trading Cards
Collected all T-shirts
Earned an S Rank on all Ranking Battles
Admired all slightly saucy costumes
Collected half of all Trading Cards
Earned 10 Gold Medals on Free Fight Missions
Reflected Destroyman's Destroy Canon with your Beam Katana
Reflected Dr. Peace's unblockable Quick Shot with your Beam Katana
Purchased all of the merchandise at AREA 51
Collected half of all T-shirts
Completed all Training Sessions
Obtained all Beam Katanas and parts
Earned 25 Gold Medals on Assassination Missions
Reflected Bad Girl's human clones with your Beam Katana
Defeated "Henry" for the True Ending
Learned all Wrestling Moves
Earned 14 Gold Medals on part-time jobs
Defeated "Jeane"
Used all toilets
Defeated "Alice Twilight"
Defeated Rank 2: "Bad Girl"
Learned all of Lovikov's techniques
Earned 5 Gold Medals on Free Fight Missions
Defeated "Matt Helms"
Defeated Rank 3: "Speed Buster"
Broke 510 destructible objects throughout Santa Destroy
Defeated Rank 4: "Harvey Moseiwitsch Volodarskii"
Earned 10 Gold Medals on Assassination Missions
Defeated 30 enemies in a row without taking any damage
Defeated "Kimmy Howell"
Defeated Rank 5: "Letz Shake"?
Defeated Rank 6: "Holly Summers"
Used whatever means available to beat 510 regular enemies
Earned 1 Gold Medal on a Free Fight Mission
Defeated Rank 7: "Destroy Man"
Earned 5 Gold Medals on part-time jobs
Defeated "Nathan Copeland"
Defeated Rank 8: "Shinobu"
Broke 51 destructible objects throughout Santa Destroy
Defeated "Skelter Helter"
Defeated Rank 9: "Dr. Peace"
Earned 1 Gold Medal on an Assassination Mission
Used whatever means available to beat 51 regular enemies
Earned 1 Gold Medal on a part-time job
Defeated Rank 10: "Death Metal"