Jump Ultimate Stars/Obtaining gems

Gems are required to unlock most of the in-game content. You can obtain gems in various different ways.

Completing missions
Upon completing missions, you gain gems. The easiest missions to gain gems in are: All of these missions are item battles, where you need to collect the items before the end of the time limit. Simply KO the other opponents and collect their gems, as you will gain them regardless of if you clear the mission or not.
 * Red: Eyeshield 21's world, mission 2
 * Green: Ninku's world
 * Yellow: Gintama's world, mission 2

Match Ranking
In J-Arena, complete all three Match Rankings (Point, Survival, J-Symbol). Once you have done so, Champion Match Ranking will be unlocked. Upon completing each of these rankings, you will gain 500 red, green, and yellow gems, as well as 200-500 of the other kinds.

Multiplayer
You will gain gems for each multiplayer game you play.
 * 1st place: 50 Red, 50 Green, 50 Yellow, 10 Blue, 10 Pink, 10 White
 * 2nd place: 30 Red, 30 Green, 30 Yellow
 * 3rd place: 20 Red, 20 Green, 20 Yellow
 * 4th place: 10 Red, 10 Green, 10 Yellow

J-Quiz
Once you have completed the story mode once, you will unlock J-Quiz mode. While it appears to be useless unless you happen to know how to read Japanese, pressing on buttons and randomly getting good answers will get you gems. For each correct answer, you will get 5 Red gems, 5 Green gems, and 5 Yellow gems.