Mass Effect Legendary Edition

When you are able to travel to different systems with the Normandy go to one of the random ones not linked to the main quests, When you find one you can land on go to it. You can then immediately return to the Normandy and repeat. You can just keep landing on the same planet for it to count.

One you are able to travel with Normandy, pick four planets that are not part of the main storyline (you'll easily recognize them as they are marked). Land on them and after you visit the fourth world, this achievement being the second exploration-oriented will pop-up.