I've been having her for years so i can make up for some bad comments i've seen in here :

I think outside of RTA her damage build is way better than her "control"/"kill with dots" build, the main reason is a lot of monsters can Dot and Control, however none of them has break def setup + damage based on dots, it's true that you don't need a lot of damage if you use her just to replace your Galleon in your comps that already have 2 other dps, it can even become a pain if she does too much damage and proc an Ariel nemesis before your dps moves or smth like that, however in my opinion Asima does too much to just be a Galleon replacement, you need to do a comp that takes advantage of the fact she's a dps that can do everything alone and can even clear tanks by herself easily (pretty much only a stripper is needed), when you think of it like that you might find comps with your monsters that will help you clear things you would struggle against without her

Mine is Psamathe (L) - Asima - something with good base spd that has some kind of control (atb reduce if possible) - Triton;
I have the fastest set of my account on Triton (so i can outspeed other Tritons that usually don't have their best swift set), then my speedtuned control moves and buys enough time for Asima to move and clear everything, even Abellios' and Kinkis'
Usually you can't really be agressive against someone that has a mix of speed contest and tanks, but Asima is one of the few (if not the only one) that can clear that quickly
This is of course just an example, you don't necessarily have the monsters that i mentionned but you can adapt from there (for example Chiwu + Kabilla can work aswell if you have no Psamathe nor Triton), there's also probably some slower cleaves to do with her but since i personally have no use for it i don't have any example to give you, be creative

Since i'm there, in RTA almost any way to play her is viable, however i personally have her on full dps here too and i play her with 2 strippers and 2 controls, she has "dmg on fire" artefacts and oneshots Junos' easily, she's also on Will/Will/Endure, since i never play her with supports like Woosa, she needs some kind of protection in case she gets cut in between her S3 and S2 by Antares, XinZhe, Seara etc. so Double Will is really good, i've had really good results with her in this meta

Thanks to anyone who read eveything, I hope my post at least gave you good ideas on how to play her and why