First you need to destroy the ship's mana shield (blue bar) then suck away its willpower wit the deckgun. Then you should see the smoke-stack fall off the ship, revealing a glowing, flashing "weakspot". make sure you avoid the fireballs (most ships shoot three at a time but it's easy to discover the pattern and dodge them) and shoot the weak spot until the ship's HP is zero.
Next - and you gotta be quick about this - man the flak gun, because the ship will morph into its final flying form. Shoot it down before it flies away and you can get a HP+ pickup which will increase your maximum dive depth. Good luck!!!
