TLDR: Only if you like her. She's a fairly basic Chaos DPS that isn't outdamaging any of the 2.X DPS we've gotten so far, and considering she's free you have even less reason to actively use pulls on her banner. With that said, she IS our first actually good Strike focused DPS so if you like that style of gameplay she is a better option than OG Helot for example. With that all said, she doesn't actually do anything to staple the various Strike characters together... so don't expect her to be the bridge that finally lets you run Helot Lotan together.
Mouchette is Morimens' first playable collab character and a return to the thought-to-be forgotten Strike archetype. To briefly summarize, all her cards are considered "Strike" cards and her kit is based around spamming as many Strikes as you can per turn. Every 2 Strike cards played will cause her to perform a pursuit attack (a new mechanic that is essentially an extra free attack commonly seen in other turn based games) on a random enemy, up to 4 times a turn. Note that this is ANY Strike card, not just her own. Finally, she has a variety of Strike based buffs, including a teamwide Strike damage buff based on her own ATK.
Alright, let's get to her dupes; they're pretty good, as expected of an arc 2 character. E1 gives her some crit scaling for stacking Death Resistance, which is kind of important considering DR is her main stat. E2 lets her clone another Strike card with -1 cost, which is extremely good. E3 makes her Exalt grant her +1 hit count on all her attacks, which is also extremely good. Overexalt further improves her Death Resistance synergy by making her exalt deal additional instances of damage for each time DR activated. The obvious entry point is E0-E1, and the stopping point is E3, but she is a member of the "prints her own Aliemus" club so spamming OE is a lot easier for her than it is for most awakeners. I wouldn't say her dupes are more worthwhile than, say, Kathigu-Ra's, but you wouldn't be "bricking" your account by pulling for them. If you're unsure just use shop dupes as usual and save your pulls for a character you don't get for free.
Mouchette is arguably the most flexible DPS of 2.X so far, despite her Strike focused gameplay. Since every awakener has a Strike in their kit (and some have more), she can easily find teammates to work with her. Instead, you should consider what realm you pair her with. Pure Chaos is an option as usual, but she doesn't really need to restrict herself in this way. She does have perfecty synergy with Lotan though, as both perfectly compliment each other with Strike spam and Strike card creation. The obvious Caro teammate is Helot; while Helot herself is effectively a non-character, her Exalt providing Strike %DMG up synergizes perfectly with Mouchette's Strike flat DMG up; Helot can also fish Mouchette's cards out of the deck for her. Of course, this would necessitate using Thais, which is very awkward for D-Tide when she's already in demand for multiple other teams, but perfectly fine for story progression. From Aequor, there's only really Goliath who has a Strike via his Exalt. She does have a lot of damage instances for red stance tentacles I guess? Finally, there's Ultra, who has... Tinct I guess? It's a decent synergy, since Tinct can discount Mouchette's cards, remove debuffs, and give her Crit Rate, while having some big damage Strike's via her Exalt's permanent Strike up. I wouldn't call this particularly noteworthy, but it at least exists.
The better way to build her is to treat her as the main DPS. She does have strong built in scaling and Aliemus gain, so all you really need is some solid teammates to pair with her. Feel free to pick whatever you want, as all the typical recommendations work well with her. Caro is probably the best of these if only due to Helot's massive buff combined with manually consumed Embryos to push more Exalts out, but anything can work if you throw enough S tiers at it.
Mouchette is a very fun character; not only reviving the Strike archetype, but also introducing a new-to-Morimens mechanic in her pursuit attack. I hope we see more of this mechanic in the future, alongside more interesting collab introductions (considering their statement on the rules for collab characters, I have faith that whatever they add will actually make sense as opposed to other gacha games who haphazardly drop collab characters in without really considering the story).
Is she worth the dupes? Probably not, but are you really gonna say no to that smile?
