"You're off to Viper Manor, right? Take me with you."
If you want Nikki in your party, when you first go to Termina and need to find a way into Viper Manor, do not do anything related to Guile or Peirre, because if one of them joins your party there's no way you're getting Nikki. This is a bad thing. What you must do is go to the Magical Dreamer's ship which is docked in the far left part of town. The upper room will be unavailable to you but the lower room you can enter. Talk to the woman in the right of the room, she is the manager, and she'll mention how Nikki is gone. Miki returns then saying she followed Nikki to the Shadow Forest but couldn't go in because of guards. Miki will ask for your help; agree to help her. Then just head on over to the Shadow Forest and everything will fall into place. Before you know it, Nikki will be in your party!
To get Lime Light, Nikki's final tech, you have to wait until Serge gets his body back and you can have Nikki in your party again. Take Nikki to the cruise ship S.S. Zelbess in Home World and have him talk to Home World's Nikki. This is the resulting conversation:
After their little jam session Nikki will aquire his Lime Light tech. Now wasn't that easy?
If you want to see the Nikki's concert ending for Chrono Cross, start a new game plus (after beating the game). You need to pick Nikki as your guide to Viper Manor, and once Kid gets poisoned take the option to save her, then go to the Hydra Marsh in Home World and get Razzly for your party as well. Then with Nikki and Razzly go to Opassa beach and defeat Lavos. You'll then get to see the Magical Dreamers perform, along with their three new members: Serge on percussion, Kid on vocals, and Razzly as their mascot.