Here's an easy way to get 99 lives with team rose and team chaotic.
Team Chaotic: Go to the area "robot storm" in the haunted mansion stage. Build up their team blast using charmy and continually using thunder shoot. Their team blast will fill up quickly. Use it when dr.eggman sends another swarm of robots(around the second swarm will do) and you will have almost 100 rings already. Keep attacking even if there are no robots. When the gauge drops down to 0 it will be half filled already. Keep attacking using this method and you will have 99 lives.you might have to go through it a couple times,though.
Team Rose: Beat their story mode(it shouldn't be too hard)and go to challange. Redo all their levels but do the extra ones(the second ones without a grade)and they will have to find a certain amount of rings. It will be around 200-600 or so. Anyway, by the time you finish all of them, you should have 99 lives. If you don't by some strange happenstance, go through bingo highway(second level of casinopolis stage) and play the bingo boards. Getting bingos will get you over 100 rings automatically. Winning will get you 300 extra plus 100 for every bingo you get. This goes the same for all teams(bingo highway, not the challange)