Explore Isle of Quel'Danas

It seems that one merely has to arrive on the island to get the achievement. When I flew to the island this morning, the moment I landed the entire map was revealed and the achievement was unlocked, even though I had never been to the island before.

Link to map

Dawnstar Village (41, 32)
Greengill Coast (63, 48)
Magisters' Terrace (60, 30)
Sun's Reach Harbor (54, 33)
Sunwell Plateau (40, 45)
The Dead Scar (53, 84)

The in-game map actually has the names of every point needed, so the coordinates and the link to the map probably aren't needed.

For those of you (like me) who want to explore this before level 70:

Sorry. You can't swim there from mainland anymore. They put an inviso-wall just outside of non-fatigue waters. :(

You CAN go over to Ghostlands and EW to get those achievements before 70 (through Eastern Plaguelands), but it's a tough trek through EPL, be very careful.

EDIT: I'll do some more testing on this, since sugarnails was able to get there at 67. I'm hitting 70 soon so I'll test every level; as of 61, I still can't.

EDIT Again: You can arrive at 67 at the earliest.