Fusion Stars are items from The World Ends with You. In the DS version, they are accumulated during battle in order to perform Fusions (a cooperative attack between Neku and his partner). Only Neku's partner has the ability to accumulate Fusion Stars through their respective psychs/combos, and then only by following each psychs respective rules.
Obtaining Fusion Stars
Neku's partner can obtain Fusion Stars by navigating to the right goal panel on the Combo Map before it disappears. If they navigate to the right panel, then they will earn either one or two Fusion Stars, depending on if their guess is right on the first try. The way to earn Fusion Stars is different for each of Neku's partners.
To earn Fusion Stars when Shiki is your partner, you have to match one of the three symbols shown in the goal panels, to the ESP Card that the cursor is pointing to. Three ESP cards are shown face down at the top of the screen. When you navigate to a symbol in a goal panel, the ESP card with that symbol will be flipped over. If the ESP card flipped over was the one that the cursor was pointing to, then you earn a Fusion Star. The number of stars earned depends on the number of tries it took you to get a match. If you got a match on your first try, then you earn two Fusion Stars. If it took you longer than one try, then you get one star. When you get enough Fusion Stars, the Fusion Pin will appear. Touch it to start Neku and Shiki's Fusion.
To earn Fusion Stars when Joshua is your partner, you must match numbers, displayed at the top of the screen, with the values shown in the goal panels on the Combo Map. Each of the numbers on the top of the screen will have either a ↑, ↓, or = displayed on it. If the number has a ↓ on it, you must navigate to a value on the Combo Map that is lower then the number displayed. If the number has a ↑ on it, you must navigate to a value on the Combo Map that is higher than the number displayed. If a number has a = on it, you must navigate to a value that is equal to the number displayed. The number whose conditions you must meet is marked with a cursor. Every time you pick the correct value you earn a Fusion Star and the cursor moves on. Even if you don't get a match the cusor will still move on. When you get enough Fusion Stars, the Fusion Pin will appear. Touch it to start Neku and Joshua's Fusion.
To earn Fusion Stars when Beat is your partner, you must match up playing cards of four different suits. When Beat attacks from the ground, the goal panel has two cards that will be inserted into the top of the screen. If he attacks from the air, only one card will be inserted. A cursor marks where the cards you pick will be inserted next. The cards will stay there until you select the skull card from the Combo Map. Once it is picked, groups of cards of the same suit will disappear, giving you a fusion star each group. All remaining cards will move to the center of the screen to fill the gaps, repeating this procedure until there are no more groups (each successive chain of cards that match after previous matches have disappeared will give more fusion stars). Cards that don't match will disappear after all the matching cards have disappeared. When you get enough Fusion Stars, the Fusion Pin will appear. Touch it to start Neku and Beat's Fusion.