There's no in-game way to track your progress that I'm aware of.
That being said, you only need to kill five. It shouldn't be that hard to remember which ones you've killed, given a list to look at. Nukapedia has a list of possible targets on the page for this achievement.
Note that only Super Mutant Behemoths and Mirelurk Queens count, and that you need to land the killing blow yourself. Here's the list, which doesn't appear to include DLC:
Super Mutant Behemoths
- Outside of Fort Strong.
- West of Natick Banks.
- In the woods south of Greentop Nursery and north of Malden Middle School. Only spawns after removing a Jangles the Moon Monkey toy from a car crashed into a tree.
- West of the Suffolk County charter school.
- South of Walden Pond at a car-like Stonehenge.
- Swan is a unique super mutant behemoth and can be found at Swan's Pond at Boston Common.
- South of Recon bunker Theta.
- At the Castle as part of the quest Taking Independence.
- At the Murkwater construction site, must be defeated in order to use the area for settlement.
- Spawns at Spectacle Island once throwing the circuit breaker.
- At Nahant Chapel, nesting near the coast.
- In the basement of the Massachusetts State House.
- South of Warwick homestead and east of the Poseidon Energy plant, close to a capsized boat in the swamp.