No matter how hard I try to flail about and get myself un-stuck from the bird house, I can never get caught in the chef's riding mower. How do I fail this first, easy boss fight and earn the achievement for it?
Trim Your Moustache — Get sucked into the riding mower.
In 'Home, Sweet Home,' the last chore you're tasked with is to re-hang the bird house. When you do so, the Chef appears and tries to suck you into his riding lawn mower. If you toss the bird house onto the hook, rather than hang it while holding it, Octodad will be sucked into the whirling blades of the mower. Like the Trickshot-gun Wedding achievement, this one is a matter of practice and a little bit of luck. Make sure you're far enough away from the hook so that you don't hang it accidentally while still holding onto the bird house.