for the S3 rank up i'd say you'd want a few lvl 35 (or above if you have bought and completed the ex episodes) idols.
Your main unit has the most important bit: a pair of interest rate boost during and after the burst (Chihaya/Haruka for Vocal, Miki/Yukiho for visual and Hibiki/Makoto for dance). You should also have enough memory appeals to burst 4 times, especially if you consider Takane's burst skill. Use a slow vocal song for scoring (there is a slow one with 2 vocal stars, forgot which one it is though, use that one), if you get it to gold you can get some more score out of it. Also make sure all the tier 3 lessons are active at all times (5 stars), and give them an outfit with as much vocal as possible.
If this still isn't enough to beat S2 events, then you simply have to level up. Without getting your idols at least to lvl 35, you can forget to beat the S1, i don't think it is possible. I'm not even sure it's possible with lvl 35, you might need to get them to S rank and past lvl 35.
For the rank up festival: Don't forget you can switch out the support idols after reach song. You can also use the first song of the festival and try to make the enemy waste memory appeals and not even trying to actually win it yourself. If the opponent only has a few memory appeals left, he'll have a harder time on the 2nd and 3rd song, since he can't replenish the appeals between songs like you can. I think i only beat him once in just 2 songs, in all other cases i had to use all 3 songs, but my policy is to always keep Yukiho in the unit, so i could only switch out one idol per song.
You might also want to get all idols to at least 3 memories. This helps with the rank up festival (because you have more idols to switch in) and you'll probably have a really hard time beating the EX #4 with an idol with just 2 memory appeals, even if she is S rank lvl 35 (max level is only increased after beating EX #4, even if you have beaten the S rank up festival).
As for general scoring in your team:
Fill your burst gauge mostly using memory appeals, top off with vocal appeals, burst, rinse and repeat. To conserve memories (and get you more time to fill the burst gauge) you might want to do a solo burst with Haruka immediately on your first burst. You'll have to try out how many memory appeals you actually need, if possible try to burst 4 times. The last burst should be a Chihaya solo burst.
In my trio team with 14 memory appeals using Cosmos Kosmos i do a Yukiho solo burst, 2 Miki/Yukiho duo bursts and one Miki solo burst, that leaves me with one memory left over since i can fill the voltage gauge once with just 2 memories and the rest visual appeals. But if i do a duo burst in the beginning, i won't have enough time to fill the gauge with just 2 memories (and i think doing a trio burst somewhere leaves me 1 note short of filling the voltage gauge with just 2 memories).
I hope this helps a bit.
