During this mission, you'll need to make sure to use the touchscreen to do the turret sections. After destroying the last of the eggs, this trophy will pop. If you already did this mission and are worried you'll have to completely restart the game just for this, not to worry! After you beat the game, if you collected at least 145 Precursor Orbs, you'll unlock a Level Select. From the main menu, choose 'Secrets', then 'Level Select', then choose this mission and just run through it shooting eggs as fast as you can. If you die while doing this, you won't even have to redo any turret sections you already finished, the eggs will stay destroyed.