In Fuse story, while in Riki's case, he only enter your party before the final part of the case.Riki (00:06:40): He is available at any story except Asellus' and Red's.In Fuse's story, she'll only enter in your party at her case (can be found at Trinity Base or before the Last Battle) or after you finish her case at least once.In any of the original protagonists, she enters in your party without any issue.Emilia (00:04:04): She enter in your party as party of Arcane Gift side quest, when you try to go underground in Baccarat's parking in search for the Gnomes for the Gold Card.If you try to travel to Magic Kingdom with him in your party, he'll leave and you can find he again at Devin.

In any other case, you can find him at Devin's airport, just speak with him.In the Twin's case, if you want Blue, at the begin of the case, choice to follow him and he will enter in your party afterwards.Blue (00:02:17): Only available at Fuse's story.In Red's case, he'll enter in your party in several parts already in Alkaiser form, just to battle his bosses.In any other case, you can find him at Manhattan's airport with BJ & K, just speak with him and both will enter your party.

Red (00:01:13): Only available at Fuse's story.

Since the characters are needed for other trophies, at this trophy there will be just the list of all available characters in the game with their respective trophies (and the times in the video for each one):

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