WoWDB

While completing all four objectives in one run of  Troves of the Thunder King is possible, it is -incredibly- difficult, especially without practice. I highly recommend picking one objective and going exclusively for that objective or at least combining similar objectives (Tenwu of the Red Smoke is within 15 seconds of God-Hulk Gulkan, so these can be combined usually).

Obtain a Handful of Stolen Gems from the Treasure Saurok

Obtaining a  Handful of Stolen Gems from the Skumblade Pillager is something that (as far as I know) only occurs in the second "room" of the scenario (after the long first room and the first tunnel). There are several Golden Treasure Chests lining the walls of this room. Randomly upon opening one of those chests in this room, you will be stunned ( Suddenly, a Treasure Saurok!), and he will take the treasure from the chest and run off at an extremely high speed towards the door to the second tunnel.

There are several things to note in the Skumblade Pillager chase. He does not trigger the traps on the floor as he runs through them, but he can be stunned or slowed (and this is nearly mandatory). Also, he will automatically open doors as he approaches them, but these doors will close after 10-15 seconds. If you stay close to him, you can get a "free" ticket into the third room. However, halfway to the door to the final room, he will head into the water and take a massive jump to the top of the waterfall and you will lose your chance to kill him. Additionally, when entering the third room, you will almost always aggro the two nearby Stone Watchers (via  Eternal Slumber). Therefore, it is ideal to kill him before he enters the third room.