Hala, is it Kree You're Looking For?
Fly back to the capital in Hala to find some guards waiting for you.
Dispatch wave after wave after wave of them.
When there are finally none left, enter the building.
Stage left there are three blue-and-orange crates. Telekinect them into the nearby hopper for the pieces to a minikit.
Pull off the Hulk Handles upstage left to reveal a ladder.
As Medusa, climb it, leap across the walkway, and pull open the looped panel (you may need to smash the nearby items to get close enough).
This reveals the turbine controls. Go down and hang from the bar in front of them to slow the turbine down.
The first two laser grids have big gaps in them- wait for the gaps before jumping through. The last grid flicks on and off- jump through when it's off.
Smash four weaponless goons, then hit the button at the far end of the walkway to deactivate the turbine.
Go to the megamegaphone and use Black Bolt's sonic attack (you can either fly up or ride the platform up).
Smash some goons, then the new cracked panel at the statue base stage right.
Use the piece to build a handle for the megaphone platform,and turn it to a new position.
Sonic it again, and deal with another wave of goons. There are two electro-chargers among them, but Medusa's one-two aerial punch is good for taking them out the second their shields drop.
Proceed to the next room to confront the Supreme Intelligence, minus a few eyes.
Beat up Star-Lord. A steady stream of punches will do the trick.
When he hits zero health he'll toss a grav bomb that gives you some pieces. Build them into a boom box, which in turn triggers a dance-off. Follow the onscreen prompts to watch Star-Lord get served.
He'll break free from the mind control, and the S.I. will send out floor-based shockwaves you can jump or fly over.
You now face Rocket and Groot, who are super annoying. They both have health bars- Rocket is much weaker, so he'll probably hit zero first. However, this just makes him invincible. Also, when he's on Groot's shoulders, they're both invincible. Dodge his attacks when they're paired, and hit Groot when they're not. This will probably take several cycles.
When they're finally zero'd and restored to your control, there's another slew of shockwaves and goons. The goons keep coming, but when the shockwaves end, SI attacks with tentacles. Attack those when they get stuck in the floor.
When both are destroyed, use Rocket's grenade on the silver stump left of the core, and Medusa's hair on the pull-loop to the right.
A single Black Bolt shout should be enough to take out the core itself.
This completes the mission.