Below you will find information on the places where you can find legendary weapons and armor. Usually, these items have higher stats than the regular items in your equipment. You can collect them and use them, or you can sell them to merchants (a good way to get Elexite).
Phantom string (bow)
The bow can be found in the village of Istok, which you will visit during one of the main quests (it is located high in the mountains that are on the border between Edan and Abessa). Find the tower and climb up, where you will find the bow.
Redeemer (energy weapon)
Located on the Converter on the rooftop of Abesa North. It is best to pump over and get good armor and weapons, because strong enemies await you there. Use the elevators to get to new floors. To get to the roof, you must use your jetpack.
Archon's Might (energy weapon)
Found in the Claws Hideout, which is located in the sewers below the Domed City in Abes. You can get to this place during the "Strange Mechanism" quest. When you are allowed to enter the hideout, you can grab a weapon from one of the tables.
Bastion of Calaan (shield)
Hangs on one of the walls on the first floor of the Cathedral (located in Hort, which is the headquarters of the clerics). This is a theft, so before you do this, you must be sure that no one is around you.
Thunder Strike (Ranged Weapon)
This weapon can be found in Duke Logan's secret cache on one of the upper floors of the Duke's bunker located in The Fort (Rogue headquarters). During the day, the room is guarded by a soldier. You can kill him, but it is better to wait until the night when the soldier leaves his post. Then you must enter the fenced-in balcony.
Ignis Arthakes (two-handed sword)
You can find this weapon during the Harvest Time quest, where you will help a farmer to harvest. Go to the island next to the ruins of the Goliet Hotel. In the center of the island you should find a hole in the ground - jump there, but remember that there is a dangerous monster nearby. There you will find a sword in a stone.