I did this today. Got it first go. I used:
1. Unborn Val'kyr - 1, 2, 1.
2. Snowfeather Hatchling - 1, 1, 2.
3. Levelling pet - I used lvl 22 Nether Faerie Dragon.
1. Curse of Doom
2. Shadow Slash
3. Shadow Slash - which will miss.
Swap to Snowfeather
5. Falcosaur Swarm
6. Falcosaur Swarm - continutes
8. Falcosaur Swarm
9. Falcosaur Swarm - continues
Vinu should have died at this point. Snowfeather finished off one of the backline pets before dying. Then I used my levelling pet to kill the other backline pet.
*I was using this team for the world quest, not the Falcosaur Team Rumble - but it should count towards the quest if you follow the usual rules, i.e. summon before the fight etc.*
I used Legs (2,1,2), Lunar Lantern (1,2,2) and Sharptalon Hatchling (1,2,1)
I just kind of threw it together so I made several mistakes and it still worked out.
The general idea was to use Whirlpool when available. I didn't think about Vinu's dive and so I missed with one by miss-timing it. Otherwise I spammed pump.
Finished Vinu off with the Lunar Lantern by using Flash, Light, and then Beam until Flash is available again.
Finished off the back row pets with the Sharptalon.
I understand the fight is incredibly rng because of Vinu's brew attack, however, and I might have just gotten lucky.
Not too impressed with this strategy but tried it anyhow to give some feedback. Moves on Syd don't go as planned later in the fight, although the first half seems to be promising. Twilight Fiendling seems to be rather useless, better throw in a Magical Pet (wisp or the likes) against the flying pet. Last pet could be anything, although given the RNG on what pet is added, I'd go for one with critter attacks.