The five giant creatures that will qualify for this trophy include Super Mutant Behemoths, Mirelurk Queens and the creature known as Swan.
There is a Mirelurk Queen on Spectacle Island that you can attract by starting the engine of the boat on the Southern tip of the Island that has the Bobblehead and Fatman. There is one in the Castle during the Minuteman quest that takes you there.
Swan can be found in Swan's Pond which is near Boston Common that you will come across during the Freedom Path quest.
Here is a video from Harry94 with Behemoth locations:
As for killing these things, obviously a Fatman is your best bet but missiles and grenades will also do a ton of damage.