First room: Agility Test
As you enter this room you'll see a large platform in the middle with a giant organ pipe system going all the way to the ceiling in a circle in the middle of the room. This room is quite tricky and also quite difficult, if you stand in the centre where the metronome looking device is and stare at the shortest pipes, you'll notice a glowing plate on the wall.
As you shoot this plate, pipes will open up, as you enter these pipes they will launch you in the air. Performing a double jump after being launched will create huge lift. Your goal is simple, jump from pipe to pipe, shooting the plates in the room. After you're launched from the pipe a new plate will flip over and begin to glow, this needs to be shot before you land in order to land in a new pipe. If you fall and hit the ground the puzzle resets. Once you reach the top pipe, a portal will open in the ceiling to enter to claim your prize.
Recommended players: 2-3
Recommended loadout and method:
This one is more about skill or co-ordination. First of all, Ivara and Zephyr are relatively useful here, secondly everyone should have at least one good accurate weapon. Zephyr should do the pipe jumping while other players shoot the plates for them, doing both can be tricky. Having Ivara set up ziplines throughout the room through the middle all the way to the top is very helpful not only for other players getting to the top and into the portal, but also to prevent resetting, if you land on a zipline from Ivara the puzzle wont reset, so you can recover without repeating the puzzle.
Second room: Power Test
As you enter this room there will be a large ornate glass section in the middle of the room, with orbs in the walls. As you approach these orbs you'll see them begin to absorb energy from your warframe. If you allow the orb to drain your energy until the orb lights up, and repeat this for the all the other orbs in the room, the glass section in the middle of the room will reval a staircase leading to your portal.
Recommended players: Any
Recommended loadout and method:
This is quite the simple puzzle so there's no really necessary loadout to have here, however having a trinity to restore energy to the party is useful. Additionally Ivara or frost could help defend as you need to stand relatively close to the orb to refill it, leaving your vulnerable.
Third Room: Cunning Test
As you enter this very tall room, you'll notice a bunch of pillars, broken to reveal orokin plants inside them around the centre of the room, this room is also encountered in the second dream quest so it should be familiar. If you look on either side of the room you'll notice hanging from the ceiling near the platform you're on is two tubes containing water. If you break both tubes a sentry will spawn in the centre of the room. He'll perform a few attacks, but primarily a large energy wave. Positioning yourselves in front of the pillar-plants and dodging away so that the attack hits the plants will cause the sentry to destroy the plants, additionally you can shoot the small plates to raise platforms for a better position right in front of the pillar-plants. Once this process has been repeated for all 4 pillars, the sentry will disappear and an elevator in the middle of the room will open up leading to your portal.
Recommended players: 2
Recommended loadout and method:
Pretty much any tanky or defence assisting frame like rhino, chroma, frost, etc etc will do here. The eye hurts and seems to always proc bleed procs, so unless you do this perfectly a squishy frame is almost guaranteed to die. Having at least 2 players prevents wasting revives.
I haven't really found the best method for this. Standing in front of the pillar and crouching after he fires the shot seems to work sometimes, alternatively dodging out of the way seems to be optimal. I would also assume that the attacks would phase through limbo, allowing this to be completed easily, although it hasn't been tested yet.
Fourth Room: Endurance Test
As you enter this room there will be a large glowing platform on the ground floor. The task here is to stand on the button in the middle of the room for as long as long as possible, while your teammates shoot the panels the lasers are coming from which are located on the outer side of the spinning platform and around the room. If you shoot the panel it will turn from white to orange, and a small amount of water will fill up within a tube in the room. Once the tube is full the platform will lower revealing your portal.
Recommended players: 3
Recommended loadout and method:
Trinity or Oberon as well as any high health high armour frame is useful here. Accurate weapons with sizeable clips are optimal.
You need to tank all the lasers being shot at you on the middle platform, but the platform makes it impossible to use abilities, so you'll need someone not on the platform to either swap with you to keep the carousel going, or have them heal you through the use of trinity or oberon. The role of anyone not on the carousel is pretty simple, just shoot the plates to make them orange, fill up the water. Once person going the opposite direction of the carousel shooting the plates on it can generally manage. If you take too long the carousel will "overheat" and you'll fail the puzzle.
Fifth Room: Speed Test
As you enter this room there will be a lot of glow in the room, as well as 2 thumpers on either side of the room overlapping waves. Destroy the thumpers (not necessary, they're just annoying) and shoot the glowing plate up on the wall on the inside of the room. This will open up two doors just outside this small room that loop around in a big square shape around the thumper room that's split in two halves, and raise a pillar in the middle of the room. Approaching the red door you will step on a button which will open the door after a short delay. Inside one of the doors is a bunch of thumpers, inside the other door is a bunch of pillars that rise from the ground, and the whole ground is covered in slowing ice.
Your goal is to speed run each half, once the button is pressed and the door opens the walls will slowly close on you, you have to rush to get to the other side of that half of the loop, and press the button on the wall at the end, just above the staircase leading out. Once both sides are done, the pillar in the room will rise up leading to your portal and prize.
Recommended players: Any
Recommended loadout and method:
Limbo, with armoured agility and rush, as well as at least 20 seconds of rift walk. Simply rift walk and run through the whole thing at top speed, then deactivate rift walk and shoot the button at the end. Limbo is unaffected by the slow pads and thumpers. The only thing to worry about are the pillars, which go in a pattern, on in the middle, two on the outside, repeat. You can attempt this with other frames but the time limit before the walls close you out is VERY limited.
Sixth Room: Cooperation Test
As you enter this room you'll see a large square chamber suspended above a hole in the moons surface, with lots of plates floating in the room and stuck in the walls. Find one one of the four sides of the room a glowing button in front of the floating circular platforms to begin the puzzle. Once you stand on the first glowing button a teammate needs to step on the second one slightly in front and high up to lock things in place. Then you need to stand on one of the glowing buttons on the pillars in the four corners of the room, which will open up a hole in the wall nearby, your teammate must then enter the hole, press the button, proceed further into that holed area and drop down to press the button below the first one. Once all four sides and all four corners are done, you'll have access to the inner room by jumping up the circular platforms underneath it. Once inside you need 4 players to stand on the 4 platforms inside the cramped room for a few seconds to open up the door to the portal inside. Loki decoys do work to replace players, however I can't say if anything else will work.
Recommended players: 2+
Recommended loadout and method:
This is a pretty simple puzzle, if you're doing this with 2 people you don't need any particular frames, your frames and timed together focus abilities can press it. However if you intend to solo this, a ground unit spectre (e.g. ancient healer) will be required, as well as loki. Then simply use your focus ability to press the 4th button while your warframe, spectre and decoy press the other 3.
Seventh Room: Stealth Test
As you enter this very long room you'll see a large glowing button at one end of the room on the lower bottom floor. This room is rather simple, press the button and rush to the other side of the room, through the doors, and get to the glowing circle on the other side of the room, which will open the portal.
Recommended players: 2
Recommended loadout and method: Simply having someone stand on the opposite side of the wall on the other end of the room and having them stand on the button will make this easy for any frame. Otherwise simply playing a fast frame capable of getting from one side of the room to the other is optimal if doing this solo.
Congratulations, once you've completed all 7 tests/puzzles, you'll have the full mod set, and be able to brag to all the friends you didn't bring along about how awesome you are for totally figuring these all out by yourself.
Thanks to TheDarkstarChimaera for listing the test names. As well as all of my friends who stuck around for the 4 hours it took to get all the puzzles figured out and completed, half of which was spent searching for the one damn room that never spawned for us after 40 runs after it glitched on us in the first attempt.
This guide will be updated with images when i get the chance to do the moon missions again later today with some friends, until then feel free to post some images of the rooms that you think may be he