Gears of War 3

Start up beast with the following settings:
Difficulty: Casual
Map: Checkout (you want a small one)

You can get this while going for:

Wild Ticker: This will be your hardest kill to get, and so it's best done on wave 1. I started off as the Savage Drone and killed everyone except the last guy. I proceed to let this guy take my health down almost to the end and then downed him (don't fully kill him) then go kill yourself on a turret or a spike fence. respawn as a Wild Ticker and just walk up to the guy and kill him. It'll take some practice but this is the easiest way to do this alone.

*Also if you down a guy and die, then respawn as a wild ticker and then the guy dies (without you atacking it) it still counts for the wild tickers kill.* - Found by quinnpm

Ticker. Just keep at it. The ticker is easy to go around a corner and kill a guy. Make sure you use your run (hold A) feature. If your having trouble use the same strategy as I describe for Wild Ticker.

Wretch: make sure you utilize that the wretch can climb stuff (A) and leap through the barriers (RB). I've found that this is best on Wave 1 as well. You can use the same strategy as for the Wild Ticker, but I've found that this is doable with just normal play.

A list of each type if you want to cross them off:
Wild Ticker
Ticker
Wretch
Savage Drone
Butcher
Kantus
Bloodmount
Mauler
Giant Serapede
Savage Corpser
Savage Grenadier
Boomer
Berserker
Armored Kantus
Savage Boomer

You can also keep track of the ones that you need in the Stats & Awards / Achievements / Wreaking Locust Vengence. But this has to be done from the main menu.

*Note: some people are having a problem with the ticker and it not counting after playing on the same level. The solution people are having is just try on another map and the achievement will pop*

When trying to unlock higher trees, I found it easier to kill everybody but the last person, then let the round time out. That way you stay on the easier wave, and do accumulate the points to unlock the higher priced locusts.

Edit: Can't be done on wave one, but will work after beating wave one. I got this achievement without ever getting past wave 3

I obtained this with the help of just 1 other person. We started Beast Mode and progressed far enough into the waves to have some of the more powerful Locust available. I found it easiest to use the Drone in the beginning. Once the Berserker is available have your friend that is assisting play as the Berserker and destroy all enemies making sure to leave at least 1 one 'helpless C.O.G.' remaining. (The Berserker felt almost invincible; Typically shouldn't take more than 1 life to do so) At this time you are free to select the Locust of choice to get your kill with. Your friend meanwhile can go around the map destroying barriers/defensive objects thus providing you with extra time while you use however many attempts necessary to get your kill. I found this method very easy.

easy to get best done with 2 3 players because the wild ticker the wretch and the ticker die easily . best map is gridlock, just keep killing the cog until you reach the next tree of locust and use them one by one and it will pop soon can be done in one game of beast mode