For the trophy you have to take first place in the trial. That means you have to kill all 10 machines: 4 scrappers, 3 grazers, 2 Tramplers, and 1 fire bellowback - in that order. There is no time limit. The catch is that you can only use a generic bow and have limited ammunition: 5 fire arrows, 30 hunter arrows, and 25 hard points. Also, you do not have access to any potions, but you can use your medicine pouch.
How you do this can vary a bit, but this is how I did it.
1. It really helps to have the shield armor. You also may want to make sure your medicine pouch is full.
2. Make every shot count for as much damage as possible. Use Concentration/slow-mo and take your time.
3. You may want to scout the area before you start to see where the deadfall traps are - YOU MUST USE THE TRAPS as you don’t have enough arrows to kill all the machines no matter how efficient you are.
Scrappers: Lure them to Ikrie and shoot their power cells with hardpoints once she has frozen them.
Grazers: Shoot their blaze canisters with a single fire arrow. Once it blows they will slowly burn to death. This should take only 1 arrow. If they are next to each other the explosion will catch others on fire and you can get multiple kills. However, you must keep them away from Ikrie or she will freeze them and put out the fire.
Tramplers: KEEP THEM AWAY FROM IKRIE. Use Hardpoint or regular arrows to destroy their processing unit (belly). Once it blows they will slowly burn to death. I kept them together in a narrow passage where they spawn.
Bellowback: You can use whatever arrows you have left to destroy its gullet and set it on fire, but its tough. I lined him up right in from of the one of the deadfall traps and the trap did 100% of the job to kill him.
If you run out of arrows before you kill all the machines the trial automatically ends.