Duke Nukem Forever

This boss can be found in the chapter 'Queen Bitch', the achievement is story related so impossible to miss.

But when you first come I suggest grabbing an RPG from the left if you don't already have it. There's an ammo box to the far left and an explosives box in the middle. (For future reference).

The best way I found was to go to the far right and throw a pipe bomb at the bouncing pads then to detonate it when it's near her. This will bring down her shield, and allow you to step back and fire 2-3 RPGs before she closes up again.

During this time I suggest a quick run to the ammo box and to kill the little bug she will spawn.

You can keep re-using this method until she is almost dead. Then she will spawn an Octabrain, and will be constantly attacking you. Your best bet is to NOT fire an RPG at the Octabrain, as they'll just reflect it back at you. This will most likely lead to your untimely death, so whip out your secondary whatever it is and shoot that down.
Then it's a case of strafing to avoid the Queen's attacks, and firing an RPG between them.

Then the 40 gamerscore achievement is yours.

Here's a video I made to go in the 'Complete Insane' guide.

It should explain it all, PM me or comment if you need help

I found this battle to be very challenging.
When you enter the battle you will notice that the queen will not attack you. Take this time to fill up your pipe bombs and to get ammo for your RPG.

To initiate the battle, simply use a pipe bomb and aim it off the bounce pad to your left. (notice that there are pipe bombs and RPG ammo on the stone slab in the corner)

Detonate the pipe bomb once the bomb is close to the queen. After it goes off (make sure your RPG is equipped) back up and stand between the explosive ammo refill and the slab with the pipe bombs and RPG ammo. You should notice that the Queen is centered up between two rebar pipes (remenicent of goal posts) aim the RPG and you will be able to get 3 shots off before she covers up.

Then quickly run and fill up your bombs and continue to the EDF ammo box and refill your rockets.

Wait until the queen fires a pregnator then use a pipe bomb to kill it then quickly return to the left of the screen, rinse repeat until the queens health is about 1/3rd left. This is when octobrains spawn. Use the pipe bombs to deal with the octobrains, takes 3 pipe bombs (on hard) to kill them. Then use your rockets on the queen (in that same goal post spot).

Don't use rockets on the Octobrains as they will just throw them back at you.

Take your time and don't take stupid risks and this method should net you the victory reletively easy.

WINNER