Dungeons are spread out across the maps and will not show until discovered. Generally located on the perimeter of the map, with the exception of Shifting Sands where four dungeons are located down the central line.
There are 17 in total, In order to earn the achievement you must complete each dungeon once.
The secondary objectives are not a requirement. Unfortunately simply discovering the dungeons is not enough, every dungeon has both a level requirement as well as prism requirement and on top of that in many cases you will be required to locate a number of power cells in order to open the dungeon door. Usually these power cells are located in the vicinity of the dungeon, however in the case of the
Pit of Oblivion they are spread out across the map. A video guide for acquiring those particular power cells will be at the bottom of the page.
The Following is a list of dungeons their location and level/prism requirement to access:
Granite Steps:Tyrants Forge - Level 25 Prisms needed - 75
Lonely Basin:Pylon 512 - Level 3 Prisms Needed 1
Cavern Rush - Level 4 Prisms needed 4
The Brood Hive - Level 5 Prisms Needed 4
Repository Blitz - Level 10 Prisms Needed 8
Crucible - Level 13 Prisms Needed 8
Proving Ground - - Level 16 Prisms Needed 15
The CradleAssembly - Level 10 Prisms Needed 8
Core Foundry - Level 10 Prisms Needed 6
House of Steel - Level 25 Prisms Needed 10
Shifting Sands Forsaken Halls - Level 13 Prisms Needed 16
Armory Flux - Level 16 Prisms Needed 9
The Warren - Level 16 Prisms Needed 15
Acid Marsh - Level 16 Prisms Needed 17
Obsidian Run - Level 16 Prisms Needed 11
Coliseum - Level 22 Prisms Needed 12
Pit of Oblivion - Level 25 Prisms Needed 20
Pit of Oblivion Power Cell locations. Hope this helps I spent over an hour trying to find all the cells.