After the version 1.1 update, there is a new enemy added into the game, the Unusual Hilichurl - Menace of the Mansion. From the version 1.1 developer live stream, we know that this hilichurl is essentially the company's CEO, Liu Wei, or nicknamed "Big Wei", in hilichurl form. He is meant to be a stress relief enemy for players to beat up.
There can only be 1 Wei hilichurl at a time. Once you defeat him, he will spawn again somewhere on one of the locations. After you defeat him a second time, he will respawn 12 hours later, for 2 more attempts. If you want to rush the achievement for defeating him multiple times, you can join another player's world.
The unusual hilichurl is not a tough enemy to fight. He only has about 3 attacks. 2 of them involve him throwing items from his suitcase, which can sometimes be primogem(s). There is nothing you can do about the Primogem, other than to watch it get shattered when it hits you or the ground.
After defeating him, he will leave a very important item behind.
The first time you defeat him, you will get an achievement: "...Well, That Was Strange," giving you 5 whole Primogems. The next achievement requires defeating it 20 times, and the last one is 50 times. Getting all the achievements will give you a total of 35 Primogems.
One of his spawn location is next to the shrine that's close to the Anemo Hypostasis, in Stormbearer Mountains.
Windrise is the area just outside of Mondstadt. He can be spotted near the tree close to the Statue of the Seven - Anemo.
Cape Oath is the area of the Electro Hypostasis. He has a chance to spawn near the edge of the cliff.
Spotted near the broken bridge that's in Stormterror's Lair. You can reach there somewhat easily by teleporting to the center of the area, then use the wind upcurrent to flu up and glide to the location.
He can spawn near the edge of Andrius' colosseum, but not inside the area. This location is in Wolvendom, south west of Mondstadt.
Dadaupa Gorge is west of the Electro Hypostasis boss. He is close to the teleport waypoint shown on the picture above.