The strategy is to fire a teardown arrow into one of the Disc Launchers located on the Thunderjaw's sides. One teardown arrow should dislodge a launcher completely, making it yours for the taking. Try to distract the beast away from the launcher, then run over and pick it up.
Sunstone Rock is automatically obtained when you reach the city. You can find it to the far West of Meridian. When you get near the city for the first time, it will be under attack by a Behemoth. This will trigger the beginning of the quest, so kill the Behemoth then head inside the city.