Here is the full list of all 11 Minigolf Adventure trophies - there are 6 bronze, 4 silver and 1 gold.
Unlock all the balls
Complete at least one level of each world
Collect 100 gems
Collect 12 stars
Collect 60 stars
Collect 120 stars
Collect 4 gems with one shot
Hit the ball with maximum force 20 times
Collect all gems in the level and lose
Play a game in Hot Seat mode
Play a game in Race mode