Farming Simulator 17

This solution is a couple years old now and the game has changed a bit but most importantly, DANIELVS found that you can just give the cows water & grass and they'll breed well enough without having to give them power food and hay.

The rest of this guide is what I originally posted back in June '17. If you're just after the achievement then give thanks to danielvs for saving you a couple hours of work. If you want to know how I think they intended you to do it originally (ignoring the fact that I used the money mods to buy all the cool equipment) then read on for how to do it with all the extra hassle.

The guide for sheep and other comments I've seen say that the breeding achievements have to be in a single session. The good news is that I popped this today and it was cumulative across sessions. I'd bred 6 cows in a session last week and it popped when I bred 14 more today.

Cows consume alot of resources so if you are going to try to get this quickly, whether in a single session or not, you'll need to do quite a bit of prep.

Some recommended mods / equipment to gather everything and feed your cows:
1. Peecon Biga Mega Mammoet - 64K capacity power food mixer
2. Joskin Q-Big Liner 32000TRS - 32000 liter water trailer
3. There's a shovel bucket mod you can put on a loader that lets you carry ~11500 liters at a time which really helps on making power food.

Here's what I basically did to get 14 cows in one session - since it doesn't have to be in one session (would've been nice to know earlier!) you could do alot less prep and gather alot of this food while breeding instead of doing it all ahead of time like I did.

I bought fields 25, 27 and 28 by the cow farm.
I planted grass on 25 and 27, wheat on 28.
I erased the upper right edge of 27 by the water trough and build two haylofts.
I also built a water tower just south of the water trough across from the haylofts.
I set the speed to 120x

For hay:
I ran a tractor with a hired hand with a mower & tedder on 25.
When the mower was halfway through I'd start a tractor/hired hand with a windrower.
After they were done I'd let it regrow and run them both a second time to make the rows fuller / reduce trips with the loading wagon.
Then I'd go through with a big loading wagon to pick up the hay and filled the two haylofts.

For grass:
I ran a forage harvester with a large tipper starting on the bottom edge of field 27. Even before I erased the edge of 27 I found the 'L' shape often confused hired help and they'd get stuck or declare they were done after one or two rows.
At 120x by the time he'd harvested 56K grass (and I noticed) I could drop that tipper off and hitch up to another one and the grass was already regrown to hire & start mowing again.
I used several of these grass tippers for silage and then had a couple trailers of grass for food parked by the eastern trough.

For straw:
Harvest field 28 then run a loading wagon to pick up the straw and fill the haylofts. I also dumped a wagon full in the storage shed next to the silage.

For Power Food:
Put a Peecon under the hayloft and fill it to ~42% with hay (~28K).
Drive over between the silage & straw.
Using a loader with the 11.5K shovel, add two shovels of silage and one shovel of straw to the Peecon. This will bring it to the right ratio and about 98% full.

Prep before I bought any cows:
After filling 4 Peecons with power food I refilled the haylofts with hay and straw just to be sure (some of the hay was probably needed, straw wasn't).
I had one tipper of grass parked on the eastern trough, another on standby.
I had one wagon of hay parked at the trough
I had a big loading wagon full of straw parked by the cow shelter ready to unload.
I had one Peecon parked by the cows, 3 more on standby.
I had the 32K liter water wagon at the western trough.
I bought 100 cows.
I then cycled through vehicles and filled up the water, hay, grass, straw and power food to 6 days (that took 3 of the 4 Peecons because I was mostly using power food for the hay needs).
I refilled the 3 empty Peecons using the same method as above while time passed.
I only bred 14 cows from this setup before the achievement popped so to get 20 you'd go through more than I did. But, to breed 15 took me about an hour (after way more than an hour of prep time obviously) and in that hour I emptied one straw wagon, one grass tipper, one hay wagon and at least a half dozen Peecons of power food. I was mostly using power food to meet the hay needs as I didn't bother trying to fit a 2nd hay wagon at the troughs - it was easier to just use the power food wagons even though they were more time consuming to fill.