Slime Rancher

Fastest way I found to get chickens involves unlocking The Overgrowth as quickly as possible. This area only costs 1,795 n to unlock so it shouldn't take you long to get it. The Overgrowth has a stupidly high spawn rate of chickens and no slimes to eat them before you can get to them making it ideal for this achievement. It also only spawns full grown chickens so there's no wait time for chicks to grow up. Immediately suck up all the chickens you can find in this area.
Now create a coral and fill it with as many meat eating slimes as you can find. Pinks are everywhere so I'd recommend using them but feel free to use whatever you'd like. More chickens should have already spawned while you were doing this so suck them up as well. From here just run around the area sucking up the chickens as they spawn and if you run out of chickens, either go sleep until day or do something else until more respawn. The chickens respawn quickly however so you may not even need to do that really.
This area is very helpful and saved me tons of time gathering the supplies to pop the meat eating gordos.

Short version: Save 1,795 n > Unlock The Overgrowth > Suck up chickens > Create coral with whatever meat eating slime you want > Suck up more chickens > Feed slimes > Repeat the last two step until the achievement pops.

There's no real fast way to get this.

I would suggest having Pink Largo Slimes

Then build a Coop with Roostros and Hens in them.

Then every now and then check for duplicate Hens or Elder Hens.

After that feed those duplicates to the Pink Largos.

Repeat until you get 100.