The Tallneck and and Bandit Camp are pretty straight forward. I found getting 1st place in the 3 hunting trials challenging, so here's how I did it.
1. Control. You have to use the Stormslinger to shock machines to death. You need to kill 6 "minor machines" (watchers and scrappers) and 1 ravager. Don't try and use stealth, just hit the ground and start shooting as fast as you can. There are watchers and a scrapper or 2 right where you land, but a ravager will soon come over. When he does, concentrate on him, because his attacks will slow you down the most. Once you finish him off, get the rest of the minor machines you need. You may need to run to find some more as they will not all come to you.
2. Onslaught. This one will have you fighting groups of machines in 3 different areas. What eats up most of your time here is moving from area to area. Overall advice - never stop moving. Even while you are fighting, keep moving along the path towards the next area. Don't wait for machines to come to you - run to them. Don't waist time picking up anything. Use weapons with a high fire rate. I used primarily the rattler (modded for damage), the forge fire flamethrower, and a couple bombs from the sling.
As soon as you land 2 watchers will come out of the gate straight ahead of you. I managed to take them both out with a single sling bomb. Then run to the gate where you will meet 2 more. I killed them quickly with the rattler. Then run up the path to the longleg and more watchers. Concentrate on the longleg first then the watchers. The rattler made quick work of them. Continue running up the path as it bends up to the right. Just before the next gate you will face scrappers and watchers. Its a narrow path so I was able to finish them all off quickly with the flamethrower. Though the gate is another longleg and some "minor machines". I used the rattler on the longleg and rattler/flamethrower on the others. There is a larger machine (ravager I think) on the far side of the water and possibly a watcher or 2 if they didn't make it to you yet. Stay out of the water as it and the ice chunks will slow you. I stayed along the right side running to the ravager and killed him with the flamethrower.
3. Chieftain. This trial has you go through the same 3 areas as Onslaught - so keep moving along as fast as you can. Right at the bottom of the rope are 2 scorchers. I found this part the most challenging and time consuming because their attacks are savage and I don't like using the mine launcher. You will notice that one of the scorchers walks towards and away from you and ahead on the left is a deadfall trap. Time your slide down for when he is walking away and nearing the trap. Shoot the trap which will do descent damage and it will knock off his launcher. As soon as you release that arrow, start shooting Tearblast arrows to knock off the other scorcher's launcher (it will take a couple). Then run and use the launchers and sling bombs to finish them. Honestly, this fight was ugly for me and I took a lot of damage. Maybe you can find a better strategy.
When the scorchers are dead run through the gate and head up the path. There are 2 fire bellowbacks. I finished them both off pretty quick using only sling bombs and targeting there back and chest. All the while I was firing, I was moving along the path towards the next area.
Through the gate you will find 2 frost claws on the far side of the water. Run along the right side, up over the ice block, to just get in range of the first one. I killed him using only sling bombs. The other one goes all the way around the water counter-clockwise, so he never bothered me until I was finished killing his buddy. I just turned around and lobbed bombs at him until he died. I had to do a lot of crafting of bombs in the last 2 areas. On my 4th try I got first place with 5 seconds to spare.