Which Machines fall under each category?

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:

• Broadhead
• Charger
• Grazer
• Lancehorn
• Rockbreaker
• Scrapper
• Snapmaw
• Trampler
• Glinthawk

Recon:

• Watcher
• Red-eye Watcher
• Longleg

Combat:

• Ravager
• Thunderjaw
• Stormbird
• Sawtooth

Transport:

• Shellwalker
• Fire Bellowback
• Freeze Bellowback
• Behemoth
• Strider

Not Applicable

• Corrupted Machines
• Corrupter
• Deathbringer

Unclassified:

• Stalker

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.