To get into Halsey’s lab, load up Rally Point Charlie on The Package on Legendary. This can technically be done solo, but is much easier with a partner (or 2ndcontroller) because if you die playing solo after hitting the switch it reloads an earlier checkpoint without the switch activated. So that is how I will describe it. Once you load up RP Charlie, make sure you grab a Jetpack by the door to the lab.
Fight off the enemies until they stop being brought in by Phantoms. Once the area is clear, go straight out from the door and all the way down to the far side of the battlefield (across a bridge). You should be on a large platform where one of the Wraiths hangs out during the fight. Go up the ramp at the rear of the platform and down to the far end from the top of the ramp. Use the jetpack to get up on top of the fence around the area with the long tubular tanks. Hop off the edge to land on a wire mesh platform below. Now drop off so you are falling in the 10-second kill timer area outside the wall.
As you fall, slow your descent by hovering with the Jetpack so that you can interact with a switch at the base of the wall to the left, near where one of the diagonal supports meets the lower portion. This opens a door on the far lower-right side of the building where Halsey’s lab is located.
You'll respawn on your partner. Facing the door where the yellow ‘Defend’ objective is, turn right 90 degrees and go to the end of the building and drop over the ledge to the lower area/ground. Ten sword-wielding Elite Ultras will come out of the door that opens. Deal with them and enter the door. As you move forward and cross a certain point it will teleport you into a long hallway with no ammo or grenades (to prevent our typical Halo game-breaking shenanigans). Head to the end of the hall to enter the hidden tribute room/lab and pop the achievement. You can activate a switch by the door in here tonend the mission as well.