I just beat the S2 rank up without much trouble.
First of all: New Skills are unlocked upon reaching S2 rank.
As i said earlier, all idols are level 40. The description when selecting the job says following: When they start the burst (i only saw yukibro's post afterwards), it lowers your rate, lowers your voltage (to about half when it was full before their burst) and destroys your memory appeals. So i don't think they get stolen. Also the burst skill acting on activating the burst is new and it makes it impossible to counter their skill effect.
On the first song i simply overpowered them cruelly with my best team (Yukiho, Miki, Azusa using Kosmos Cosmos) even though 2 were wearing the wrong outfit, i beat them with 114k to 70k.
On the second song i went in with 7 vs 7 memory appeals and they more or less forced me to loose the song, they went all out and i didn't stand a chance.
For the third song they only had 1 memory appeal left, so i could beat them easily since i had 7.
On that last song i made an observation: my voltage bar was almost full (as well as theirs) from the second song, so i bursted very early. I was countered by them, but i still had 7 memory appeals left, my rates were about 90% as they always are when you are countered, my voltage bar was empty anyway. So it seems enemy burst skills don't activate during a counter. On the S3 rank up festival, the voltage destroying effect doesn't activate either when you are countered.
Knowing this also probably is the trick to beating Jupiter: Burst before them, it is worth it up to a cost of 3 memory appeals, maybe even 4. But burst in such a manner that they will be able to counter you, not that they burst after your own burst is done and you still loose the memories (unless you go all out and can burst another time before they get to burst). This also means you should also use burst skills that work during the burst, Chihaya, Miki and Hibiki probably are a good choice.
Edit: But i think we should move this discussion to the gameplay thread.