There's a number of things you can do to get the Remu puppet. If i'm correct, Reimu should have some level 60-68 ish puppets, the highest levelled one is Reimu.
Now what you want to do depends on your stance towards these games in general, I need some more information. If you just want to clear Reimu, no restrictions to gameplay, you can simply try to outspeed the Reimu puppet by grinding some levels. Make sure you have a 'sound'-type attack on your anti-reimu puppet. When it comes in, sacrifice your current puppet to it, and bring in your counter. You outspeed Reimu and OHKO with basically any sound move if it's the power variant due to the 4x weakness. As you're high enough level, the Def variant shouldn't be able to KO you back anyway (don't get damage on your sound puppet!). As a note: I used a speed Miko (didn't have Byakuren yet) at this point in the game which came as some nice help against reimu. Now if you want to beat her more 'fairly' by using puppets of the level you should be when facing her (about 50-65 depending on the 'cost' of your puppets and how early you filled out your team), you'll have to have a decent setup for it.
There's many strategies you can do: There's plenty of puppets that can just wall a Reimu, a few stand out:
- DYuuka can hit back hard with After Move, and anything a Reimu form does to her is low damage due to massive FDef.
- DLunasa can switch in to PReimu, tank a second hit, and KO back.
- DKanako, DKotohime and HEirin can stall a Reimu easily in several ways
- Any ghost type can switch in to her Fighting moves.
- Any void type can switch into her Illusion moves.
And there's stuff that's dangerous to her, like:
- PMystia walls fighting moves, and is fast and has STAB sound attacks. She will outspeed after a turn or two as well with Up Tempo.
- AMerlin can also have STAB sound attacks at somewhat less power, and completely blocks Fighting attacks, which you can draw out using a trick detailed below.
- SMiko has a nice typing against Reimu and can hit her with Sound attacks. Also has Up Tempo which means after 1 turn you outspeed Reimu almost guaranteed.
- SYatsuhashi has Resounding Spirit, which means her Void type moves get 1.3x power and become Sound. Because her type is sound, they also gain STAB, which means a 1.95x power boost. So Frenzy Ensemble has 195BP and is at least x2 effective on all Reimu forms. That is rather dangerous. She´s also fast because of being a speed form...
Here's a couple points that can help you:
- Using a fast fire puppet you can inflict the Fox Fire move (Burn & Weakness) on Reimu, crippling her. You can also use Miasma which takes less turns to kill, but you will need more powerful walls then.
- You can stall by using the AI's poor prediction skills: It will always use a super effective move on you if that's available. So if you for example have a DMomiji out when PReimu switches in, PReimu will use a fighting-type move next (guaranteed). A switch to a Ghost type will cause her to waste a turn.
- Spirit Barrier is useful to stall further.
- Use entry hazards: If you're trying to kill her with plain damage and can't quite get enough, try using Mine Trap while one of her other (less dangerous) puppets is out. This will get you some initial damage on Reimu. Better still, Reimu has no puppet that can absorb Poison Trap which you can exploit as well.
- Drain Seed is incredible vs. the AI for obvious reasons (it won't switch usually).
- If all else fails, there's always WTF-Boom (Absolute Devotion). That will kill pretty much anything.
- Level 19 Momiji -- Fear ARON tactics.
By the way, if Reimu is being troublesome to you, better prepare, because Shinki&Co which come after the cave you get after Reimu are much harder to beat.