Here is the full list of all 36 Super Hyperactive Ninja trophies - there are 20 bronze, 10 silver, 5 gold and 1 platinum.
Unlock Yukiko
Get killed by a Ghost
Get killed by a Ninja Dog
Use a Mizugumo to walk on water
Try to perform a fighting game special attack
Unlock Kumo
Use a Take Away Coffee and complete the level
Take a nap
Get killed by a Mokujin (Seriously?)
Enter into Hyperactive Mode
Perform a jump
Take a step
Complete all the trophies
Clear a cursed level
Pick over 9000 coffees
Stop time
Clear all levels with an S-rank
Defeat the Shogun
Clear a level without stopping once after entering Hyperactive Mode
Clear a level without picking a single coffee
Find a map to a new place during a level
Use Yuki Onna Breath to freeze an enemy
Use a Ninja Cloak to avoid an enemy
Use a Katana to kill an enemy
Use a Ninja Suction Cup to climb a wall
Clear a level with Ghosts without dying once
Unlock Kamomitsu
Unlock Yaiba
Unlock Kyu
Unlock Aragami
Unlock Jack
Unlock Ace
Hit a Shuriken with the Katana and kill a foe
Clear a level with an S-Rank
Die 1000 times
Get more than 100000 yen