There are four trophies regarding killing one of every type of Machine in each category. However, there is nowhere in-game that tells you what category each Machine falls under. The most information I've been able to find was in a teaser that introduced a few of the Machines and categorized them.
The teaser categorized the Stormbird and Thunderjaw as Combat-class Machines, the Behemoth as a Transport-class Machine, and the Snapmaw as an Acquisition-class Machine.
I also assume that Watchers and Red-Eye Watchers are Recon-class Machines, for obvious reasons. However, this only covers 6 of the 24 types of Machines, excluding Tallnecks (you can't kill these) and "Corrupted Machines".
The reason I ask is that I managed to go the entire game without killing a single Broadhead, which kept me from getting the "All Acquisition machines killed" trophy, which surprised me, because I didn't realize Broadhead was considered an Acquisition-class Machine (I really don't understand what makes it that, either, but I digress…). That said, which Machines fall under the Acquisition, Combat, Recon, and Transport categories?
Best Answer
As a start, I'll be compiling the machines per category here. These are gained from various sources around the Internet, as well as my own experience. Some are still as of yet unclassified, as their roles could be considered for multiple classifications.
Acquisition:
Recon:
Combat:
Transport:
Not Applicable
Unclassified:
Of course, the easiest way to get all the trophies to pop is to just kill one of each type of machine. As Vemenous mentioned in the OP, corrupted machines do not count towards these trophies.