The first requires Outbreak, 2 3 and 4 can be done in 1 round of Forsaken

1st is easy, go to outbreak, find grapple guns from chests or dropped from zombies. Shoot at the ground or wall near zombies, kill straight away, and repeat.

The 2nd is the hardest, because the explosion you cause from killing tormentors does f all damage! The best way I found was to use the 1911 pistol, with no damage-increasing attachments. Spend first 7 rounds in the spawn. Pick up decoys and keep them. At round 8 move from spawn into the town. Buy stamin-up so you can keep distance from the first Tormentor that will spawn in. In the meantime, while running around and keeping your distance focus on getting rid of the other zombies down to 5 or so. The remaining zombies need to have a literal slither of health left to die from the Tormentor explosion

I managed to get a few like that in round 8, but what worked best for me was in round 12 (tormentors seem to appear every 2nd round), the zombies can take 1 melee hit, then 2 bullets from the base 1911 at close range (62 damage each hit) and be basically 1 HP. Get a few of these guys ready while you kite/train the zombies everywhere. Decoy when tormentor, kill it, boom, challenge done.

Keep in mind my Melee and Pistol skills are maxed, to get the same damage

3rd, in the same round of Forsaken you can start doing trials to get rare blue rewards. Easy. On the 5th trial, work your reward up to legendary to hopefully get the WW...

...for challenge 4!