Game modes that are required for this achievement are listed below. This can be done completely via single player game types against the AI. However, it CAN unlock in MP as well. Note the cautionary statement in the description for Maximalist as well. This achievement is a little glitchy and unlocks at different times for different people.
The game modes are Skirmish, Duel, Slasher, Menace, Execution, Order, and Chaos. Duel and Slasher are found in the Battlegrounds menu, Menace and Execution are found in the Minigames menu, and Order and Chaos are found in the Campaign menu. The Tutorial is technically a game type as well, but I was unable to determine definitively if it counted.
Skirmish, Duel, and Slasher all have 6 variants for placing pieces: Classic, Tactical, Random, Madness, Recruit, and Madness Recruit. If Explorer doesn't unlock from your normal games, cycle through the various placements until it does. Note that most people do not need to do this, but a certain portion have documented that in particular Skirmish (Tactical) and Skirmish (Random) have unlocked Explorer for them. It also can unlock online, so you can try that as well, including toggling Fog of War on or off.