Quick instructions on how to unlock the new character, Rex.
How to Unlock
Start a new game as any character other than MUL-T.
On exiting the life pod run around to the back and open the hatch. Pick up the fuel array and carry it to the fourth level. Careful not to take too much damage or you’ll explode and have lose the array. In the fourth level take the steam vents to the upper area of the map and find and interact with the robot.
Only the player who has a fuel array and interacts with the robot will get the new character.