Here is the full list of all 38 Hot Shots Golf: World Invitational trophies - there are 24 bronze, 8 silver, 5 gold and 1 platinum.
Purchase every item in the shop.
Purchase every piece of concept art.
Purchase every costume and color set.
Collect every star in Challenge Mode.
Perform a spiral shot in an official round.
Score a double eagle in an official round.
Skip the ball across water three or more times in a row in an official round.
Purchase all Lv3 versions of clubs and balls.
Perform a homing shot in an official round.
Purchase every type of ball and club.
Raise all characters' loyalty to max.
Gain access to Gloria as a playable character.
Collect over 50% of the deluxe parts.
Perform a rising shot in an official round.
Score a hole-in-one in an official round.
Win VS Izzak on Platinum Rank.
Sink a putt over 45 ft long in an official round.
Gain membership to every course.
Hit a drive over 350 yards in an official round.
Win VS Pandora on Gold Rank.
Purchase a Lv3 club or ball.
Collect over 50% of the special parts.
Win VS Max on Silver Rank.
Collect over 50% of the normal parts.
Purchase every Music track.
Win VS Stuart on Bronze Rank.
Gain access to Amy as a playable character.
Enter a Daily Int'l Tournament and complete the round.
Score an eagle in an official round.
Win VS Erika on Pro Rank.
Purchase a costume.
Raise one character's loyalty to max.
Win VS Pancho on Amateur Rank.
Win VS Lani on Beginner Rank.
Perform a chip-in in an official round.
Score a birdie in an official round.
Get every trophy.
Collect every crown in Challenge Mode.