Updated 05-02-2017 01:00 AM
This achievement is unlocked by defeating 50 Dragons. You can find them throughout Neverwinter, especially in the Caverns of Karrundax Dungeon. This achievement unlocked naturally without much effort as I was leveling up to 66. You can also check your status by bringing up the menu, tab over to Quests, access the journal menu, tab once more to achievements, and scroll down to Slayer. Additionally these are all the named Dragons you can kill towards this achievement outside of the queuing dungeon:
Katatheo the Proud - Stronghold Dragonflight
Oxuno The Treacherous - Stronghold Dragonflight
Chrysos The Vain - Stronghold Dragonflight
Ekdos The Cruel - Stronghold Dragonflight
The Green Dragon Volzakairs - Well of Dragons
The Blue Dragon Kradazuur - Well of Dragons
The Red Dragon Hohengroth - Well of Dragons
The White Dragon Glycamerax - Well of Dragons
The Black Dragon Rogrotus - Well of Dragons
Tiamat the five headed Dragon Queen - Well of Dragons
Halectrizar The Storm Eater - The Siege of Neverwinter Event
Kazlotar The Mordacious - The Siege of Neverwinter Event
Ikzinfraxis The Glacial - The Siege of Neverwinter Event
Phlagenthx The Cremator - The Siege of Neverwinter Event
Venitaxis The Pestilent - The Siege of Neverwinter Event
Zavarak The Thunderous - The Siege of Neverwinter Event
Eziderax The Caustic - The Siege of Neverwinter Event
Glaxenheim The Pale - The Siege of Neverwinter Event
Akregon The Pyre - The Siege of Neverwinter Event
Toxicallus The Despoiler - The Siege of Neverwinter Event
Garrundar The Vile (Level 44 Player Skirmish)
The Red Dragon Karrundax - Caverns of Karrundax (Level 54, 3 Player Dungeon)
The Red Dragon Lostmauth - Lair of Lostmauth (Level 70 Epic, 5 Player Dungeon)
The Blue Dragon Fulminorax - Malabog Castle (Level 70 Epic, 5 Player Dungeon)