Here is the full list of all 12 Golf Zero trophies - there are 11 gold and 1 platinum.
Get all other trophies.
Complete the level 41.
Complete the level 31.
Complete your first level with a cart.
Complete the level 22.
Complete the level 14.
Get gold and use only one ball in level 9.
Overcome your first enemy and ccomplete level 7.
Complete the level 6.
Complete the first level.
Get a gold medal.
Die the first time.