Here is the full list of all 37 Hot Shots Golf: World Invitational trophies - there are 22 bronze, 9 silver, 5 gold and 1 platinum.
Get every trophy.
Score a double eagle in an official round.
Perform a homing shot in an official round.
Purchase every item in the shop.
Skip the ball across water three or more times in a row in an official round.
Raise all characters' loyalty to max.
Perform a spiral shot in an official round.
Collect over 50% of the deluxe parts.
Score a hole-in-one in an official round.
Purchase all Lv3 versions of clubs and balls.
Purchase every piece of concept art.
Collect every crown in Challenge Mode.
Collect every star in Challenge Mode.
Purchase every type of ball and club.
Gain membership to every course.
Perform a rising shot in an official round.
Collect over 50% of the special parts.
Purchase a Lv3 club or ball.
Sink a putt over 45 ft long in an official round.
Win VS Izzak on Platinum Rank.
Collect over 50% of the normal parts.
Purchase every Music track.
Win VS Pandora on Gold Rank.
Hit a drive over 350 yards in an official round.
Win VS Max on Silver Rank.
Gain access to Amy as a playable character.
Use every shot type in an official round.
Score an eagle in an official round.
Win VS Stuart on Bronze Rank.
Enter a Daily Int'l Tournament and complete the round.
Purchase a costume.
Win VS Grace on Pro Rank.
Raise one character's loyalty to max.
Win VS Pancho on Amateur Rank.
Perform a chip-in in an official round.
Win VS Isabelle on Beginner Rank.
Score a birdie in an official round.