Gawain's Artifice are her burns, which makes your local galactic neighbourhood star look like a brown dwarf in comparison. Your team will quickly turn into a pile of stage girl-shaped cinders if you don't do anything about it.
Gawain is immune to MaxHP% DoT.
Anyone that can cleanse or block burn is useful. Merlin Nana, Castaway Kaoruko, and Castaway Hikari, who have burn remove/block are best here. Even though Merlin is at a disadvantage and Castaway Kaoruko is neutral, it's still possible as long as you properly protect them. The much-vaunted Awakened Shiori method is of course no longer viable with the element switch.
1) Castaway Hikari, nice and simple
Bring out a standard cloud chopper team with the other four slots, exploiting the relevant row unit skills if you need to. If using Merlin , you will have to compensate for the lower damage output with your other four girls. Solely relying on Castaway Kaoruko may be risky if you fail to draw her DoT removal act quickly.
2) How to protect your Banana
This team warrants more heavily defensive play. Use Bride's climax to defend Merlin from the first boss climax - this is non-negotiable, as Merlin can be oneshot. Make charging Bride a top priority in the first few turns.
Ignore Cheshire's taunt.
AP Down Snow White can be chained into counterheal against the boss climax for excellent results. Counterheal also works well when used with Bride's invinicibility.
Hold Merlin's burn guard and use it when it expires or if Merlin is in danger of being defeated. Snow White's evade can keep Merlin alive through the second climax, and Bride can protect her from the third.
Merlin's climax buffs are very useful and should be used.
If using Cupid instead of Cheshire, Cupid's Aggro can also be used to protect Merlin.
3) Midrow stacking solves all the world's problems, again
Merlin, Cheerleader Tsukasa, Kung Fu Mei Fan, and two mid row offensive US with high US levels which stand in front of Mei Fan. One of them may be subsituted for by US21 cloud offense US.
Focus on charging Mei Fan and using Tsukasa's buffs. Unleash Mei Fan's climax on turn 5 at the latest.
By high, I do mean high - 16-21, please.
This team consists of Cupid, one backrow cloud attacker, and one backrow passive taunter, to activate Cupid's unit skill. Keep Cupid's provoke up, heal, and use DogRuko's 3AP and climax only.
Using Musketeer Hikari and two backrow fodders, including one passive taunter, is also possible, but less reliable, as Musketeer Hikari may die before the second backrow fodder does. This, however, lowers the US requirement on Cupid by half, assuming that Musketeer Hikari is US21.
1) Prince and Princess Knight
US19+ Snow White, and one Flower or Midrow defensive unit skill stick. Preferably in front of Snow White. During the initial turns, prioritise using Prince's cleanse to remove Gawain's opening act burn.
Once the US stick perishes, chain Snow White's Counterheal, AP Down, and either Prince's heal or cleanse depending on which would mitigate more damage (depending on the current burn tick and the health of the two girls).
When Prince's CX is available, use it. During the 3 turns where burn is blocked, Prince's heal can be used instead of alternating heal and cleanse.
Snow White' counterheal must be available for Gawain's CX. If Gawain will cast her CX that turn, delay your own CX activation to avoid the risk of not drawing the counterheal.
2) Disney Princesses' Duet
Use Salai Mahiru's cleanse as soon as possible. This protects the back 3 and encourages the two front unit skill fodders to perish. Salai herself will die the moment Gawain reaches her, leaving you with just Snow White and Sleeping Beauty.
Once this has occurred, the move order will be Counterheal - AP Down - Negative Effect RES once every three turns, whilst the other turns use Sleeping Beauty's sleep and brilliance strike instead. This ensures that Gawain can never place burn on you while maximising damage output.
Activating CX is only safe under the conditions that (1) Snow White is at nearly full health; (2) Gawain has just used her CX the previous turn; and (3) You have two turns of Negative Effect RES. This is because counterheal must be used to intercept every Gawain CX. It is not necessary to activate CX at all using this method - it only reduces the turns needed for completion.
Queen of Hearts Yachiyo easily replaces Sleeping Beauty in this setup, except that negative effect RES can be used every turn since it's 1AP.