After quite some struggle I managed to beat the final boss here are some tricks I learned on the way. After the tricks you will find a "walkthrough" with optimal positions to make each room easier. Also SPOILERS
Disclaimer: This Minigame is incredibly hard compared to the rest of warframe and to beat it you will require hours. If you complete the challange you will be rewarded with a poster.
First of: the weapons. There are 3 of them and you only want the blue powerups (lasers) they have the highest range of all weapons and on the highest level they can hit enemies above and below you. Dont pick up more than 3 Powerups because you cant improve a level 3 weapon and risk getting a yellow or red powerup.
There are several types of enemies. The yellow and black drones shoot passively without taking your position or speed into account. All the other enemies (apart from bosses) try to anticipate your movement. This can be used to your advantage by flying on the ground and holding down.
There is the possibility of dying due to collisions during a room transition. To prevent this dont hold right while flying into a wall and dont get to close to the left side of the screen. In the second room there is a flipped desk on the floor that instantly kills you when you fly into it. Better keep your distance.
Now to the walktrough. Since powerups drop randomly I will include solutions for different weapon levels in the description of the first rooms. Remember to only pickup powerups while they are blue. Also keep the fire button pressed.
-In the first room fly to the right and a little bit to the ceiling. Then shoot the first drone and dodge its shoot. Then hold left and down, dodge the 2 shoots of the crew member while holding down and kill him.
-During the transition into the second room hold right and fly into the right screenborder. (Level 1 Weapon) When you enter the room position yourself in the middle of the doorframe and kill the lower drone then move left and up at the same time bait out a shot of the second drone and kill it afterwards. (Level 2+ Weapon) Move above the upper end of the doorframe and try killing both drones at once. (Level 1 Weapon) Then fly up to the ceiling kill the turret, move down to the ground and kill the two crewmembers. (Level 2+ Weapon) move to a medium height and focus on dodging bullets. Now only drones and a turret remain. To kill them move to the right till you reach the last third of the screen and kill the drones before they enter the screen. You should have enough time to pickup some powerups before killing the turret at the ceiling.
-When entering the third room you should already have weapons of level 2 or even 3. Now move to the bottom right corner and keep holding down till the moa dies due to a collision with your wyrm. Then move up and to the left while aiming at the turrets and crewmembers with the diagonal beam. In case you miss some of the turrets you dont need to kill them since they cant aim to the right. The crew members however have to be killed. Stay on a medium height till all the drones are dead and then drop to the floor and keep holding down. You can move to a ditch in the ground and shoot the moa while it is still off screen.
-In the 4th room you will encounter all dronetypes and a some of them will spawn one after the other while you are allready in the room. Those new spawning drones are your top priority because they activly aim at you. When entering the room stay on the hight of the door frame and move up slowly while tapping up and down to distract the spawning drones. After they stopped spawning you can move to the right slowly while killing the last drones.
-The 5th room is the hardest one and I havent found a 100% consistent way to do it so I will list two options: The harder one requires you to stay on the floor move close to the first moa while holding down and baiting out a stomp. Then you can fly up and kill it and repeat the process for the next moa. The second option is to fly straight up while the moas are still off screen and to fly circles on the ceiling to make it harder for the moas to hit you. They will however still shoot at you during the transition into the boss room so be warned.
-When you transition to the first boss room there is a turret shoting at you. Stay at the ceiling while holding up and when you see an option to move into the room with the turret take it. Enter the room by moving around the upper end of the doorframe while staying as close to it as possible. Then stay at the ceiling till you killed the turret and move on to the first boss.
-The first boss is a ambulas. When entering the room stay at the upper left corner in case the boss starts with an early attack and then position yourself in that way that the horizontal beam and the first lower diagonal beam hit the ambulas. The boss can perform two attacks. During one attack he drops bombs on the floor and during the other one he jumps forward and spawns some mitter blades. The first attack can be dodged by moving up and left, while the second one can be dodged by holding down. After you killed the boss move on to the next transition.
-Before the final boss there are some additional turrets to kill. Stay at the ceiling and kill the first turret off screen then move to the ground and fly up the stairs while taking care of the second turret. The last two turrets have to be killed while dodging.
-The Last Boss is a Helios. Move up till you can see the ceiling and move to the right till you can see the boss. The Boss has two main attacks. During one of them he releases a bullet storm where you have to move trough a corridor between the lasers. When you dodge the bullets while holding your horizontal position you should automaticaly dodge the barells and the particles they create. The second attack consists of multiple voleys of shots where you can move a little bit to the left to create larger openings between them. During the fight focus only on dodging the diagonal beams should kill the boss eventualy.
I hope this helps.