They win the battle on the planet. It takes a day to have everything under control and he loses two mages, but it was a foregone conclusion from the beginning, and they manage it with fewer casualties among both the Andalites and the Yeerks and hosts than the median projection. Lots of infrastructure damage, but that can be repaired.
Leareth spends the time reviewing the not-quite-finalized next movements, doing message-Gates, nailing down where to go next to collect more Andalite fleets - they can take them from this system, which was previously heavily guarded since it was a juicy target for the Yeerks, but the Yeerks are going to have other things on their minds and then aren't going to have ships anymore.
Seventy-two hours after Nayoki's shuttle touched down, he Gates them out, leaving behind a single Andalite ship to guard the planet and mostly-intact Pool ship, still in orbit but without any of its Yeerk crew. Just tens of thousands of baby Yeerks in a pool, which a couple of grossed-out Andalites do the required maintenance for.
...
The third planet on the list, ordered by proximity to the Council base, is a nine-day hyperspace journey for the courier ship that might or might not be on its way there. They reach it after five.
This time Nayoki's gambit with the decoy Yeerk ship fails when the ground station asks for authorization codes, which Mhalir would know but she and Leareth do not. It's a touchy few minutes, Nayoki's ship is not well shielded enough to hold off the other Yeerk ships firing on her, but Leareth worked out a version of the comms spell that he and Nayoki and a handful of his other mages can use to reach each other even when one of them is in a ship in hyperspace, and so the Andalites jump early. The orbital battle is a lot messier but they win. This world doesn't even have a Pool ship in orbit, just a big pool on the ground, and all of the Yeerk ships are destroyed. They lose one of the smaller, less-well-shielded Andalite ships as well, which would have been several dozen casualties, but Leareth does a frantic last-minute Gate from the Dome ship, it's just barely within range, and they get half of the Andalite crew off before the shields go down.
A couple of courier ships get out, as the Andalite fleet is jumping in, so now Leareth has to make a second list of possible destinations and timelines to juggle.
The fight on the ground is comparatively easy. Several of the ground bases surrender even without compulsions.
Nayoki's Yeerk ship takes a lot of damage and they have a choice between delaying, or leaving it behind. Leareth thinks they should leave it behind; the other Andalite ship also left behind can work on repairs, and maybe he can make a trip back for it later, or maybe not. He does an extra few Gates to borrow the second jump-capable Yeerk ship from the Council planet.
They regroup for several days and move on.
...
Leareth pushes some of the Andalites to drill Gates hard. He probably can't teach them to do the starship-sized kind, there are just too many prereqs there, but at this point he has message-Gate thresholds and video footage of their locations on most of the worlds he needs to keep communicating with, so those don't need to be unscaffolded, and they can be accomplished on reserves and the node-generator alone, they don't require bizarre concert-work with a computer-controlled artificial channel. The only reason Nayoki and his other mages haven't mastered them is the hyperspace routing, and Leareth wonders if most humans just don't have the innate spatial skills for that. Andalites have better mathematical skills on average, though, and maybe they can get it down in time to actually help.
...
Matirin asks Leareth if he's pacing himself enough. Leareth thinks he is. He feels tired all the time but it's not even just the Gates, those he can space widely apart so that he's never utterly exhausted, and none are as bad as the first one from Earth to the Andalite homeworld. (In hindsight it might have been better overall to do two Gates and rest for a few candlemarks at an intermediate point.) It's just draining, wrangling so many moving pieces at once, getting news from light-years away of battles that could have gone better if he'd had more time to plan or given them more resources, and so far Leareth isn't sure he's made any obvious mistakes, but that doesn't help with the bone-deep weariness. He wants the war to be over.
...
The fight for the Taxxon homeworld is a nightmare, half because of the orbital shipyards, half because most of the Taxxons are voluntary Controllers. Leareth just feels far worse about that. He really hopes they can just give the planet back to the alliance of Taxxons and Yeerks, afterward, but given the constraints they're under elsewhere, they can't leave it in the hands of the current Yeerk administration and risk it ending up as a supply of reinforcements.
It's not a fight he feels particularly good about, afterward. But they win.
They garrison the planet, send messages, Gate in more Andalite ships from other frontiers, and move on.