Inside The Computer

This achievement is quite hard but still very doable.
As a general strategy you should always try to run in circles, kiting the boss behind you and collecting all blue buff orbs.

General tips:

• You can mostly ignore all the adds spawned by the boss and the pink orbs.
• The only other thing you should do damage to (apart from the boss) is the bullet target thingie that spawns occasionally. Leaving it alive for too long will debuff you very heavily.
• When going from one phase to the next everything is instantly despawned. That included the green walls. Use that to your advantage!
• Make use of your shield (middle click) and your teleport (hold Q) to survive situations you would otherwise not survive.
• Your AoE attack (right click) does not deplete your ammo --> Always use it on cooldown to damage the boss together with your normal attack.

The boss has 4 phases:

Phase 1:
Easy peasy. Just follow the advice above and you are good.

Phase 2:
Starts at 0% of the boss image health.
Not much has changed compared to phase 1.
Just continue doing what you did in the previous phase.

Phase 3:
Starts at 75% of main boss health.

In this phase the boss splits in copies of itself. The copies do not have much health and can be killed in about ~10 hits. These copies spawn in each corner of the platform so try to position yourself near a corner so you can start damaging a copy as soon as they spawn. Try to nuke down 2 copies before the other 2 can reach you and then start kiting the remaining 2. It is important to not get overwhelmed by the increased amount of adds that 2 boss copies are spawning. This phase ends when all 4 copies are dead and the main health bar at the top is at 0%.

Phase 4:
Starts at 75% of main boss health.

In the beginning of this phase the boss is invulnerable for 30 seconds. Use this time to collect as many orbs as possible and to kill everything else that the boss is spawning. In this phase all of the boss' attacks do double damage (unconfirmed), so try to dodge everything as much as possible and use your shield almost on cooldown. Apart from that this phase is not that different from the first 2 phases.

Phase 4,5:
Starts at 50% of main boss health.

This is where things get crazy. In addition to everything else the boss is already doing it now spawns laser beams that damage you and are very hard to avoid since they move very fast. Just try to stay calm and keep collecting buff orbs and occasionally damage the boss. Especially the green walls can be very deadly now since they only leave you with a 4th of the platform to dodge all attacks. Try to make use of your teleport and shield in situations like these. The bullet target thingies have the highest kill priority in this phase since getting debuffed will be your death sentence. You will need a good portion of luck in this phase since you will die quite fast if you make a mistake.

The first 4 phases are pretty easy compared to the last one. If you can consistently reach the last phase you will eventually have that lucky try and kill the boss. I think it took me around 10 last phase tries to kill it. So just keep trying. Good luck!