Is there any way to complete it? I've destroyed the Destroyer, but by the time I do it's too late, the Bio-Warhead has been released.

So how do I complete the mission? And kill the Warhead?

I Find that the Best way is to fly a Thunderbolt

First target the big ship and hit it with your torp on the fly, afterburn until your in range, launch torp then target the bio-weapon missile and hit aterburn untill your in range and hit it with guns/missiles untill you destroy it.

it's also best to ignore EVERY thing else until this is done ( asuming that you did'nt ignore them before), after that do as you like to rack up the kills or head home.

Your = you're but thanks.