No its not impossible, just get into a battle with Rikku and Tidus on the front line, get the third person to escape, wait for Rikku to take damage then get Tidus to heal her. Rinse and rpt about 20-30 times. You can do this in one or two battles (don't kill the fiends straight away obviously!)
Its also a good idea to go back outside Guadosalam and save the game immediately after leaving the Far plane and before talking to Rikku, because then you can try all 3 different responses she makes. But you can talk to her more than once anyway, like you can with Lulu.
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