After you've reached level 50 and completed the main story quest, you can start the quest chain to get your first Legendary Armor and Weapon. This quest chain will require you to complete all 3 level 50 dungeons, do some traveling and some mob farming (300 for Armor, 600 for Weapon), so be prepared to take some time to complete, but its well worth the rewards!
To start this quest chain, you'll need to talk to Type Gi-3 Orha in the Sealed Sanctuary where you complete your main story quest.
She will give you the quest Athlon Rashon Judge and ask you to find the Rashan Agent near Humbaul Fortress in Athlon.
The Rashan agent can be at one of several locations around Humbaul Fortress, so check the mini-map to check each location until you find it. The item you're looking for is Hidden Rashan Communicator.
After that, you'll need to complete all 3 level 50 dungeons, either solo or in a party.
Once you've completed all 3 dungeons, go back to the Sealed Sanctuary and talk to Type Gi-3 Orha to complete the first quest.
The next quest you'll get is Ragferant Rashon Judge. Just like before, you'll need to go to Ragferant region and look for the Hidden Rashan Communicator, which can be located in several places around Rumbling Axe Outpost.
This time when you find the Hidden Rashan Communicator, it will turn into a Rashal, an Agent. Talk to Rashal to continue.
You'll be asked to go back to Type Gi-3 Orha in the quest log, however, this is incorrect. The quest locator on the map has you going to Humbaul Fortress to talk to Iyeta.
Talk to Iyeta to finish that quest and get the next quest called Athlon's Atlite. The reward for this quest is a choice between 3 Legendary Armors (one for each of the Evolved classes). You'll need to kill 100 of 3 types of mobs (total of 300) all in Athlon. Check mini-map for locations of the 3 types.
After killing the mobs, go back to Iyeta at Humbaul Fortress to claim your reward. Congrats! You've got your Legendary Armor.
Next is your Legendary Weapon quest. Iyeta will give you the quest called Greleaf Atlite.
This time you're required to kill 200 of 3 types of mobs (for total of 600). However these mobs are more challenging. While it is still possible to solo these mobs, its recommend you find a Party or even Expedition to kill them as it will go much quicker. (Everyone who has the quest will get the quest item per kill, so don't worry about having to share the quest item loot.)
To get to Greleaf, you'll need to go to a special teleporter called the Hunting Ground Teleport Manager. These teleporters are located at Humbaul Fortress in Athlon and Meiville in Ragferant. Fortunately you're already at Humbaul Fortress!
Talk to the telepoter and she will take you to one of 3 Hunting Grounds. These are level 50 areas that have daily/weekly repeatable quests. You'll want to go to the Greleaf Hunting Ground.
Once you arrive, might as well pick up the daily/weekly quests as you'll be killing the same mobs for multiple quests.
Find the 3 areas the mobs are on your mini-map and start grinding away! Once you've killed all the required mobs, go back to Iyeta in Humbaul Fortress for your reward!
Select one of the 3 Legendary Weapons (One for each Evolved class).
Congrats! You now have your first Legendary Weapon!
The Quest line continues on, but the rewards are not as good as these Legendaries, so continuing on is optional.