What the achievement asks
Bomb four specific targets in Freehold while flying a parrot. Five points, account-wide.
You get the parrot from a quest, it gives you a Vile Bombardment ability, and the four targets are scattered among the pirates below. The bombing is easy; knowing which four objects count is the whole thing.
Getting into the air
The parrot comes from Swab This!, a Tiragarde Sound world quest at Freehold. Alliance players can also reach it through Rodrigo's Revenge, the ordinary quest, so you do not have to wait for the world quest to come round.
Mount the Riding Macaw and you are up.
The four targets do not exist until you are on the parrot. Flying over Freehold beforehand to scout them shows you nothing, which is a trap worth avoiding: there is no point going to look first.
The four targets
The clip covers the whole run in one pass, which is more useful here than four separate coordinates: the parrot flies its own way and what matters is the order you take them in.
Doing both at once
The achievement and the quest are independent. You can clear the four targets first and finish the world quest afterwards on the same flight, which is the efficient way round.
Pirates you bomb from a long way off sometimes stay grey and appear not to count. Wait a moment: once their nameplates turn red again the credit lands. It looks like a bug and is not one.