Map: The Covenant
1 - After deactivating the first tower, there is a part in the level where you have to fly a Hornet to the third tower. As you hop into the Hornet, the title If You Want It Done Right will be displayed—if it isn't, then no skull will appear.
2 - On your way to the third tower, you will see the second tower (which was disabled by the Elites). This is also the tower with the Terminal. Fly over to it.
3 - There is a long, flat, semi-enclosed part of the tower that extends out over the ocean. There is a very tall ramp that leads up to it. At the end of the extension you will find the Thunderstorm Skull.
Note: Restarting from Rally Point Alpha allows you to go to the skull's location, but no skull is present. Also, the "Too Close to the Sun" achievement can be unlocked from the skull location.