If you're as much a completionist as I am in games, then you'll have a lot of fun with Diablo III—a title that's literally (metaphorically) burdened with more secrets than you can shake your fists at.
Among the secrets you'll have fun uncovering are a host of secret dungeons that only have a small chance of appearing each time you enter certain parts of the game—and every part of the game seems to have a few of these around.
You'll need to visit each and every single one of these secret dungeons and read various books and manuscripts found throughout these areas to acquire the related achievements.
We'll start off with the game's first three acts and their secret and not-so-secret dungeons.
To acquire this achievement, you must visit all of the following locations.
Much like Act 2 in the previous game, Act 2 of Diablo III takes place in the desert—this time in the sands surroundings the city of Caldeum. The sands hide a number of secret dungeons that you'll have to revisit multiple times to uncover.
Notably, the Fowl Lair and the Veiled Treasure can only be accessed through a special portal device that spawns very occasionally.
To access this dungeon, you must kill a unique Rockworm.
Located in the Dahlgur Oasis, the only way to access this dungeon is to activate two levers to open the door.
Opening this tomb requires that you hit a lever by the entrance.
Killing a unique Rockworm opens this dungeon.
Located in the south of the map, you must first save a merchant from ghosts.
Accessible only through the portal device.
Accessible only through the portal device. It's even rarer than the Veiled Treasure.
Now that you're done with Act 2, it's time to move on to the third and penultimate act in the game, which takes place on the battlefields of Arreat. Most of these locations, like those in the previous acts, can only be found occasionally, so you'll have to revisit this location multiple times (preferably on different characters, so you don't burn yourself out) to visit them all.