Subtle, but the shyer Bandori girls like Rimi, Kanon and Rinko being able to step on stage at all and perform.
In the second season, Rokka perfectly nails an epic guitar solo. It’s not made clear if she improvised it, but if she did so, and on the spot in front of so many people, that’s a huge achievement.
In the third season, third episode, Rokka auditions for Raise A Suilen, playing an arrangement of their song "R-I-O-T". Except she plays not only the guitar-parts, but the bass and keyboard parts as well, leading to LAYER commenting that she "half expects her to start singing as well".
Poppin' Party's live collaboration with OxT on "Kimi Ja Nakya Dame Mitai", and with Fripside on "Only My Railgun" (which is the closest to a Love Live! collaboration as Fripside's vocalist Nanjou Yoshino voices Ayase Eli).
Season 3 has several.
The challenge that CHU2 issues for RAS vs. Roselia. Both bands give it their all, but RAS pulls a 50 vote victory, which CHU2 had Lampshaded earlier by pointing out to Yukina that whoever went last tended to get a boost by virtue of being freshest in everyone's mind.
Though momentarily stunned by the defeat, Roselia emerges at the end even closer to each other and stronger for it, even as RAS suffers under CHU2's dictatorial style.
Poppin'Party, by virtue of staying out of the fray and just performing their best and having fun, in other words, just being themselves, rise to the number 2 spot in the polling, earning the right to participate in the finals.
Afterglow chose not to participate, because they already had a prior commitment on the day of the finals, and because getting to Boudokan was a special goal of theirs, and doing so as part of a contest felt like cheapening that dream. But a conversation between Ran and Yukina suggests that Roselia's leader felt that if Afterglow had participated, they'd have been a force to be reckoned with.
It’s not made clear if she improvised it, but if she did so, and on the spot in front of so many people, that’s a huge achievement.