Take an M16A1, Carl Gustav and Support Marker (and recovery items).
Run underneath Cocoon immediately and attack the gas vents with your M16A1 until they're both destroyed. Beware of two things while underneath Cocoon:
1. A machine gun that may pop down at one end of Cocoon and start firing at you. You can avoid its fire by running from side to side, or out from the underside of Cocoon.
2. Cocoon may "crouch" to try to crush you. You can mash the Triangle button when prompted, but it's safer to run away (from the underside of Cocoon) if you have time.
Once the vents are destroyed switch to your rocket launcher and attack the AI Pod. It takes about three hits to decrease on life bar, so you'll need to use the Supply Marker a few times.
It has three attacks: Main Cannon, Sweep Attack and Area Attack. These can be avoided by running underneath. Additionally, for the first half of the battle (before you whittle its health down to about halfway) it will move around and may run you over. Each of these attacks can use up two rations worth of life, so be careful!
After you've got it down to a bit less than half life, it will report "Thermostat Malfunction" and thrash around a bit (so keep out of its way!) before eventually coming to a complete halt. This makes life much easier. Keep pounding the AI pod. After you've whittled it down some more a ladder will drop down and Huey or Kaz will tell you to climb it.
(1) DON'T. The machine guns on the upper decks will kill you.
Keep pounding the AI Pod to remove all its life, but try to arrange it so that you have some ammo remaining for the next bit. After its life is down to zero, you'll have a chance to capture the AI Pod, but you'll have to be quick.
Run up the ladder and turn left. Run left and jump to the next level, then turn right and ascend the second ladder. Turn right and attack the AI Pod. If you run out of rockets the M16A1 works also. Keep attacking it until its life goes to zero, then you can approach it and climb in.
If you run out of time it will reactivate with three life bars and you'll need to jump down and repeat the process.
(2) DO IT: Go up these ladders and climb to the top of the Cocoon. Once you are on top, it can only use two of it's attacks: The machine guns on top, and the missiles. To avoid the machine guns lie down flat in between the machine guns until they are done firing. When you hear missile target locked, wait for the missiles to be fired and run towards the back, and let the missiles impact on the front. In between shoot the AI pod. Rinse and repeat. Once Huey says shoot the AI pod to open, fire away on the AI pod and climb in. No risk of running out of time like this.