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