I've enjoyed reading the "two pet" strategies here for the garrison trainer dailies. I didn't see one today so I thought I'd share what I used.
First, your trainee pet may have to take a big hit, so this fight is best served for trainee pets that have 1000+ health. You might get by with a pet with 500 health if you are careful, but there are no guarantees you can keep a lower level pet alive in this fight.
I used the Puddle Terror and Spawn of G'nathus, because both have a speed advantage. That is crucial.
It is also crucial that you avoid the "big hit" that both foes can deliver. These two pets give you plenty of chance to do that.
I start out with the Puddle Terror:
1. Use Clobber. This avoids the round one "big hit" you'd otherwise suffer.
2. Water jet. The Kind and Queen will swap, so this will hit the incoming pet.
3. Dive. This avoids the swapped in pet's "big hit".
A bit of discussion is necessary here. If the Dive knocks King Floret down to the 1400 health range, the rest of the battle is easy. If it doesn't, you can either abandon the battle and heal your pets to try again, or battle on using your wits. You don't have to knock him down to the 1400 range to win the battle.
If King Floret was knocked down to the 1400 health range, use Water Jet three times to kill him.
When Queen Floret replaces the dead King, Clobber her, use Water Jet, and then Dive. She will kill the Puddle Terror at the end of the dive.
Bring in your trainee pet for a round, then immediately swap to Spawn of G'nathus.
Use Swallow you whole until the Queen has her "big hit" attack off cool down (it's her second column attack), then Dive. The dive might kill her, or you might need to use Swallow one more time.
If King Floret is close to 1500+ health after the Dive, three water jets will not kill him. Use two water jets, then Clobber.
This will cause him to switch back to the Queen.
Bring in the trainee pet and let him absorb her "big hit".
Immediately swap to Spawn of G'nathus and just fight sensibly to kill her. Timing your dive to knock her below 25% health will let you kill her on the next turn with Swallow.
When King Floret comes back in he will have 500+ health. The King is under 25% health, so either a Dive or a Swallow should kill him in one attack.
Sometimes the Queen will swap the King back in. That often happened when I had a Dive in place that would finish her off. This is bad for them, as the Dive will immediately kill the incoming King, and you have plenty of firepower between Swallow and Puddle Terror (still waiting in the wings) to kill the Queen. However, in this case watch out for the Queen to use her swap move alone. There is no one to swap in, so it just gives her double damage and double speed. Luckily, this will often happen when you are diving for the kill.
Should the Queen happen to kill your Spawn, don't despair. Even tho Puddle Terror only has 142 health, he can finish the battle. When he comes in, Clobber the Queen. One or two Water Jet's should finish her off. When the King then comes back in, Dive for the Win.
This strategy is not 100% foolproof. Crits by the Royals can cause a loss. However, this is not a drawn-out fight, so an occasional loss and heal at the garrison trainer isn't a tragedy in that case. I'd say this plan prevailed for me today at least 90% of the time.