In the interest of making as much of a one-stop-shop as possible apart from collectibles, I've compiled all 28 achievements that aren't related to the two big sets of collectibles into one video.
For A Story About My Elevator and Goats 'n' Stuff, you'll get them while working on Is That A Goat? in Goat Bay City. Head through the city and collect 5 of the batteries that aren't on the top of the hotel, placing them on the battery nodes at the base of the roller coaster in the amusement park. For the 6th and final battery, you'll head on top of the hotel, but do not use the elevator. Instead, use the mattresses on the back of the building to build momentum after a few bounces (switching to ragdoll mode helps build height) to reach the top of the hotel/skyscraper without the elevator. This will unlock A Story About My Elevator.
From there, head over to the concert stage and interact with the podium to don a deadhead mask and unlock Goats 'n' Stuff. Finally, grab the battery from behind the stage. If you've been following along with my video this should be your 6th and final battery. Place it in the battery spot by the roller coaster, and once all six are there head to the top of the coaster via the elevator. Lick the coaster car when it stops at the platform to have it carry you around the track and unlock Is That a Goat?
All of this craziness can be seen starting at the 18:40
mark in the video below.