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