Jump Ultimate Stars/Obtaining gems

Gems are required to unlock most of the in-game content. There are six different kinds of gems, three for each in game type, and three others. They are
 * Red Diamonds - Power
 * Green Squares - Knowledge
 * Yellow Circles - Laughter
 * Blue Hexagons
 * Pink Tears
 * White Diamonds - Jump

Completing missions
Certain goals (those with the gems icon on them) will will reward you with around 100 or so Gem, gems can also be found as items in battle most commonly when a battle character is KO'd, in which case they will drop gems of the same type as they are. Gems of other types can also be found in chests and boxes. 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. Note that the amount of gems obtained is proportional the attack used to KO the opponent. A will cause the character to drop 4 small gems. a attack will cause the character to drop 4 medium gems, and an  attack will cause the character to drop one large gem. Also note that like any item, gems can be destroyed by attacks and picked up by the computer players, in either case those gems will not be added to your total.
 * 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.