It is represented by a blue circle with a skull in the middle. The skull has a thunderbolt on its forehead.
The skull is found on the level The Covenant. After you take command of one of the Hornets, fly toward the second force field generator (the one the Arbiter disabled) and land. The Thunderstorm Skull is waiting at the very top, at the end of the ramp that extends over the sea. You must be playing on Normal difficulty or higher, and from the beginning of the mission. You can unlock it in solo, meta-game, and meta-game co-op. You also do not need to carry it for the rest of the level. Keep it with you until the achievement unlocks and you can quit the level. Note: this skull is easy to find if you know where to go. Make sure you stay outside when you find it and that there is a top cover. If the screen at the first part says "If you want it done right..." then the skull will definitely be there.
It is prudent that you eliminate all hostiles before landing. You are much more vulnerable on foot and a banshee can easily pick you off. Furthermore, you must collect the skull before you touch down at the third tower and after the first tower (not that you'd have the choice to do it before).
As with all of the gold skulls, activating one in the campaign meta-game will activate a score multiplier. These are useful for the Meta-Game achievements.
- There is a Terminal inside the building. There are several Elite corpses surrounding it, likely from the battle to take down the second shield tower.
- There will always be the same items in the second tower, such as a Needler, some plasma grenades, and about three dead Elite corpses.