Mesmer

(117 STR, 8 AGI, 25 VIT, 70 QCK, 5 INT, 5 DEF, 5 MND, Scratch, Rally, Eliminate, Berserker x3, Ambush x2, optional Haste and Sap)

The ultimate method is the 117 STR double-fodder Mire build. You only need one level 25 dragon for this, which is at least a boon. It's a little complicated, but works out to be the fastest. If you have an Arcane dragon, it's even easier, as they can take hits better than other elements in the Mire.

With 117 STR, your dragon can defeat any enemy, minus the Wartoads, in 4 Scratches. It takes 6 Scratches to have enough breath to use Eliminate, so in the first spawn you will be capable of using Eliminate. Just make sure that your first spawn is not comprised of a Wartoad, or of 3 physical attackers (Toridae, Shellions, Scythe and Sickle Kamaitachi). You should be able to get to speed without being defeated.

Once your breath is up, for the next batches of enemies, have your trainer use Rally on itself on the first turn, then Eliminate the enemies. Only Mossy Cerdae and Brilliant Psywurms require a Scratch+Eliminate combo; therefore, if a spawn is entirely these, you don't need to use Rally.

You'll want to target Scythe Kamaitachi and Venomous Toridae first, followed by Salve Kamaitachi and Wetland Unicorns due to their Contuse. After that, just go by physical attackers followed by magical attackers. If your dragon is not Arcane-element, you'll want to be aware of your elemental weaknesses, and target those specific magic users before others.

Keep in mind that you will not be gaining an XP chain bonus, so there's no harm in refreshing the coliseum to get a better spawn, or to restart, especially since it only takes one spawn of enemies to regain your breath. Wartoads are a big reason to restart, in fact. Unless you are leveling up dragons far higher than mere exalt fodder, so they can take more hits from the Wartoad, you'll not be able to handle them. If a fodder has, and lives long enough to use, Contuse, then use it as much as you can. This is where having Haste and Sap on your trainer can come in handy. Sap restores a small amount of HP on use, using up your practically infinite stores of breath, and Haste makes you quicker for a few turns. A combination of all of these can help you defeat Wartoads with, really, just a single dragon.