These are the items you can get post elite four, dunno about the ones after that
Globe - Use the GTS in Jubilife
Gym Statue - Get all gym badges
Cute Cup - Win grand prize in Cute Contest in Master Class
Cool Cup - See above, but Cool Contest
Beauty Cup - See above, but Beauty Contest
Tough Cup - See above, but Tough Contest
Smart Cup - See above, but Smart Contest
Blue Crystal - Meat 100 people in underground
Pink Crystal - Give 100 decorative items to people in underground
Red Crystal - Dig up 100 fossils or rare bones
Yellow Crystal -Trap 100 people.