Well, since it's a rank up and Mami is leader, he can't switch out Mami
And to elaborate a bit more on what Nakiame said:
1) Slow songs are better for scoring because you spend percentually more time bursting in slow songs. A burst always lasts 10 appeals. So if you burst 3 times in a song with 100 appeals, you are bursting 30% of the time, in a song with 200 appeals you are only bursting 15% of the time. And since the score of your appeals is basically the same for each song (e.g. if you get 100 points per appeal with a certain percentage on a song with 100 appeals, you will get 50 points per appeal in a song with 200 appeals) slower songs yield a higher score, but it's more difficult to burst as often, since you spend a lower percentage of the song actually building up the voltage gauge.
2) First the memories of the 3rd girl are used up, when they are all gone, the memories of the 2nd, and only when they are gone too, the memories of the leader (in this case Mami) are used. This means you can gain more memory appeals by switching out the girls between songs. Let's assume Mami has 4 hearts, and all other girls have 3 hearts. Let's say on the first song you spend 7 hearts, that means, Mami has 3 hearts left, and the other 2 have none. You switch out the other 2, and you have 9 hearts at your disposal at the next song. A good strategy for difficult rank ups is to loose one song on purpose. I usually use the 2nd song for this. Make sure to use the 6 hearts, but no more. Try to force the opponent to spend a bunch of their own memories. And on the 3rd song (after switching out again) you have 9 memories to go all out with.
4) The opponent's burst skills don't work if they counter you. This means you need to burst before them, they might counter you, but your burst gauge will still be at least partially full. These voltage draining bursts can't be countered, no matter what you do. So if they burst before you, you can forget your voltage gauge and you'll need to start over. Keep in mind that duo memory appeals give much more voltage than a solo memory appeal, and a trio memory appeal gives even more. So it's usually better to find the right timing and do a duo or trio memory appeal to fill your voltage gauge before the opponent. This become even more crucial for the one rank up (S2 i think) where the opponent's (Jupiter's) burst also kills 3 of your memory appeals. For that fight, do whatever it takes to burst before them, make sure they can never burst without countering you. If you expect to be countered, burst with an idol where you get some benefit DURING the burst, and not only after. Which leads to...
3) Burst with Hibiki if you expect a counter. Ritsuko's burst skill sucks if you only do solo bursts, it's usable for duo bursts and it's really strong for trio bursts. you will hardly have the opportunity to do duo, let alone trio bursts on a difficult festival, so Ritsuko isn't a good choice if you have trouble with a festival. For scoring, you should use one of these pairs: Yukiho/Miki (visual), Makoto/Hibiki (dance) or Haruka/Chihaya (vocal). The burst skill of the first idol of these pairs raises the percentage of the corresponding appeal by a huge amount when the burst is complete (and thus not countered). The burst skill of the second idol of these pairs increases the corresponding appeal DURING the burst. So the best scoring strategy is to burst with the first idol, then use a triple memory appeal and do a duo burst with those 2, repeat for as how often you can afford. And then burst on the last appeal of the song with the 2nd idol of the pair. Of course you can make trio (or duo/trio and the beginning and end) bursts if you have the memories to do that. Unfortunately, you can't really pull this off during a festival/rank up due to your opponent. But if you can pull of a burst with Yukiho (which is not countered), then do a trio memory appeal and burst with Miki, you can rack up a lot of points, since the visual appeal will be extremely high during Miki's burst (replace Yukiho/Miki with the other 2 pairs as necessary/desired).