Here is the full list of all 13 MiniGolf Tour trophies - there are 1 silver, 11 gold and 1 platinum.
Collect all other Trophies
Unlock a hole effect from the customize menu
Purchase an item from the shop
Unlock a trail from the customize menu
Unlock a ball from the customize menu
Unlock an avatar
Collect at least 4000 gold
Achieve 1st place in tour 4
Achieve 1st place in tour 3
Collect at least 2000 gold
Achieve 1st place in tour 2
Achieve 1st place in tour 1
Complete the tutorial