There's many different ways to trick or force Hunters into falling off the ledges of Mission 6. I've managed to do this once, unintentionally, on Legendary difficulty in co-op, and the other two times where intentionally on easy riding solo.
The first time in co-op, I was positioned a platform away from the Hunters and my co-op partner was idol & away back at the first platform
I'd honestly forgotten about this achievement at the time and as the Hunters tried to attack me from a platform away, I was just hurling grenades and firing away at them with my Battle Rifle. One of them got a little too close to the edge and as I started firing my Needler in its direction, the Hunter simply tried to evade by dashing to its right, and then fell to his demise. Achievement Unlocked - 20G
Revisiting the mission (
from rally point delta), I put together a video this time recorded on Easy. The achievement doesn't specifiy which difficulty the mission needs to be on so I'd recommend sticking it on easy too. The Chief comes equipped with a Jetpack for the mission which comes in handy against the Hunters.
Once you reach the platform where the Hunters are, take one of them out first so you can focus soley on just the one. The Hunters don't always react the way you may want them to when using gun fire against them, so the best bet here is to use their melee attack against them. Constantly put yourself in danger by staying close to the Hunter until you can get it close to an edge. You'll find that the Hunter likes to back away from YOU (strangely) so once it is close to an edge, quickly switch sides with the Hunter so then its next melee attack will result in the Hunter falling off the edge.
This can seem a little bit tricky to do but it's really not that bad. With the difficulty being set to Easy, the damage taken from the Hunters Melee is light. Make sure you use your Jetpack to get back onto the platform should the Hunter melee you clean off of it. If you die, either when the Hunter does too or just by accident, the checkpoint will restart you at the point where the Hunters spawn in. Dust yourself off and try again.
Be sure to take a look at the comments section of this solution for some more tips & tricks on how to make these Hunters drop to their death.Check out this video for more details and help on how to get these big guys to fall to their death: