HUMANKIND

First of all: of course, play on Hamlet, just one standard AI and preferably on Blitz or Fast speed (so everything will be built and researched quicker), normal/large map, 3 continents, New World and 70% water. This way there is a chance you will end up on 1 continent, the AI player on another and you will still have at least 1 continent left to discover. This will just make it a race to get there first.

To get this you need to get in a boat as quick as possible. I believe this is only possible in te Ancient Era, so get there asap. You are able to build harbours sooner, in the Classical Era. Again, build those asap.

Try to look at the research tree and spot the harbors AND the sailing in there. These are two different researches (Harbors = Classical, Sailing = Ancient). You can click those specific researches and the whole road to get there will be scheduled. For this achievement, I advise to do so, so you will invest all research in the right ones.

In the meantime, scout with your armies everywhere, mainly along the coast. You might already be able to do some new land or coastal waters. Hopefully, you will be the only Empire on the island, making your life much, much easier.

Once you have those Harbors researched and built, keep armies right next to it so that once you have Sailing, you immediately can board them and set sail.

Now it is just a matter of sailing around till you find a new continent.

Good luck and happy sails.