You're going to need solid DPS, with SBs. Leave SUP at home, because it's useless. You'll need a healer, maybe two, depending. If your strategy involves a particular SB, you may need an EntrustBot.
Focus on the Magicite for which you have the best elemental coverage. For example, if you're drowning in Water SBs, start with Liquid Fire (who is, coincidentally, one of the easier Magicites). Once you've taken one Magicite down, do it a few more times to fill out your Magicite deck, then start working your way around the circle in a clockwise manner, using the Magicite you receive from one to help against the next.
But first step? You're going to spend a lot of time tweaking your team. You're also going to need an individual team for each Magicite. You're also going to avoid using the Optimize command when equipping, because you'll be focusing on element/status resistances, not pure stats.
Have fun. I still haven't beaten the 3-star Light and Dark Magicites.