I used the Teroclaw but subbed in Ikky for flock and the Skywisp Moth for my third, with 2, 1, 2. The Moth gets swapped in first. Just switch to Ikky and use flock. Once Ikky is dead, use Call Lightning and Reckless Strike. Both those should be buffed from flock and enough to kill him.
Strategy worked well on the first try. I had to use an H/P Mech Axebeak as that was all I had. It still worked correctly, but that might have been due to my using an H/S Highlands Turkey in place of Plump Turkey, since I don't have a plump turkey. Not sure, but everything worked fine. Thanks for the strategy!
Yeah, it works fine with an H/P Mech Axe so long as the Flock bird you're using has the same hp (there are none with higher hp). That means any Health breed of crane chick, turkey or chicken (except Bush Chicken).
By far the best I've found to use with an H/P Mech Axe though is Direbeak Hatchling. Predatory Strike then Falcosaur Swarm leaves Bucky with so little hp that Haywire only needs to hit once.
And for those with a P/P or S/S Mech Axe (1400hp), you can do the same with a Sharptalon Hatchling.