I'm not very experienced in this fight so there is a lot of uncertainty here. Its important to mention that for Rain Speedrunner role you will need to do the 5 min version, which also means Diva Skills won't work.
Here the Z-Sigil won't affect the set or weapon used.
The weapon of choice is either Divine Galatine or a Thunder Evo. In my opinion Galatine is better since the para is really useful. I will still need more attempts to know if Long or Very Long is better but currently I'm leaning towards Long.
Sigil 1: [ SnS Up 15 | Beam Slash | Element 12 ]
Sigil 2: [ Element 15 | Element 15 | Element 15 ]
Sigil 3: [ Element 15 | Element 15 | Element 15 ] or [ Element 15 | Duration 12 | Wait Time 17 ]
Since I haven't fought this monster much I will show you two sets. One uses SW and the other doesn't, the SW version will deal more damage but in the limited experience I have it's also way harder to play. And since SW is not at all required to beat the time, I created the other set. It could also be worth to drop Obscurity since getting the first PD on the intro is very difficult.
You have enough time to take both the Thunder Attack Fruit and the All Element Drug after entering the area and get the PD, if you skip the cutscene immediately.
Take the SW Potion after the PD.
I don't have enough experience to explain any specific move yet. Once I optimize this fight more I'll be sure to update it here.