Every time a character levels up in the game, they will gain some Skill Points (SP) that they can distribute to learn skills. All SP is predetermined when you level up, which caps at 600 when you hit level 80; if you do 4 Rebirths and reach level 80, you will have a total of 760 SP to distribute. There are 8 different skill trees to put your SP in, but it is not possible to get 100% in all skill trees at once.
As you purchase skills in a tree, you will gain access to more. However, there are two in each skill tree that are only unlocked once you complete the right Resident Request. Whenever you reach 100% in a skill tree, you will get a small star next to that tree on the menu, and the stars will stay there even when you rebirth. When you master one skill tree, you will get the Bronze Star trophy, and when you master all 8 skill trees, you will receive the Gold Star trophy.