Here is the full list of all 23 Starwhal trophies - there are 8 bronze, 7 silver, 7 gold and 1 platinum.
Play 100 rounds of Versus
Stab 3,000 hearts in Classic mode
Stab 1,000 hearts in Classic mode
Shatter 1000 blocks of Ice
Accumulate 4096 total points in Score Attack
Accumulate 2,000 total points in Score Attack
Die 1000 times in Challenge Mode
Obtain 32 Platinum medals
Obtain 30 Bronze medals in challenge mode
Obtain 15 Platinum in all Challenges
Obtain 25 Silver medals
Obtain 20 Gold in all Challenges
Die 100 times in Challenge Mode
Win a Versus Heart Throb match being the sole holder of the Heart
Taunt 25 times in a single match
Hold a Zone for 45 consecutive seconds
Beat your Ghost
Get your first platinum medal
Get your first gold medal
Get your first silver medal
Get your first bronze medal
Unlocked all game trophies.
Play 1,000 rounds of Versus