Honestly so far my go to tactic has been 'punch them to death with minions' and the big stuff is entirely secondary of the 'when I can afford it'. I did finish them off with a Firebase in the second round, but even without it they were out of troops, and I wasn't, so I could have just kept stabbing them to death.
The damage when enters into play effect of the Wooly is great for maintaining tempo and finishing off anything that already took damage before combat proper starts, the Mystery Ghosts don't have reliable stats but they consistently have the maximum stat values a 0 star creature can normally get so whether they're a 2/3 or a 3/2 as is the normal, either way they're good at killing the enemy, the Big Friendly Ghost/Solo Star Power combo is what lets you yeat anything you don't like back into the enemy's hand, just remember to keep one face down for when they drop down a Gunner Girl or one of their corpse monsters or whatever, and if you don't have a Solo Star Power ready the BFG's still have an attack of two so they can generally trade evenly with most of what they'd be running into.
Like, they have two ways of getting extra troops out in a single turn that we've seen so far, both the warp crews that can teleport in when something gets banished and the ghost boat that lets them play a ghost with it when it gets played, and neither of those have been able to keep the BFG/Wooly/Mystery Ghost combination from just beating their face in.
And once you get even one star, between Maidens and (if needed) Meteor Storms it's really hard to keep you from getting any more, though last game I got out a firebase just from Solo Star Powers (because those let you flip the Big Friendly Ghosts face down for the purposes of tossing anything you don't like back into their hand).
Honestly, their decks have been suffering from devoting card space to both their refineries and their own star girls in my opinion. They've got some big scary stuff and the star power to put them out, granted, but the deck space spent on that is deck space spent on 0/3 units that can't attack in the refineries and their 1/2 Star Wish Waifu cards, and a Wooly can reliably do 3 damage from their enter play damage and then finish off the refinery next turn if that's both of your opening moves and trade favorably with the Star Wishers even without the ping damage, Mystery Ghosts have 3 attack half the time, and so on, so the Refineries tend to only give out one star often anyway so aren't much better then the Star Wish girls unless the enemy already has board control, and with deck space dedicated to both cheap sources of stars that can be hard for them to get as long as I've managed to keep the aggression up.
Stirk hit 10 stars in my first game, it just didn't do them any good...
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On other stuff, looking at the new cards...
...It is a shame that the Clover Fairy's intention of 'remaining on the field to better feed the Solo Star Power' didn't survive, but hey, it's basically immortal, so that's still useful. Thorn Ward looks like it's going to be fun though. I can't personally envision playing Invader Guardians, it's just too expensive, but maybe with the Hypersummon it could be worth taking literally one of them for late game deployment? Stellar Bombardment is a good way to screw something in specific, and something like it back when Stirk had 10 stars in my first game and nothing to spend them on could have been, uh, really nasty. Hypersummon also looks like a good addition, something to spend stars on and let you sprinkle a one off or three into your deck and still reliably fetch them out once you've got the stars.
Arena wise, I'm thinking I might see if I can challenge for the Dragon Graveyard, but if someone else would prefer to take that I can switch off.