Red Dead Redemption

In order to unlock this achievement, you have to lasso one of these horses in the wild and break them. All three horses can be found in all three areas of the game, but some are more common in particular areas than others. The way to track whether you've broken them or not is to go to the local General Stores and look at the last three horse licenses available. At the start, they are all marked "unavailable". Once you've broken one of the horses, they will become available for purchase.

The Kentucky Saddler - A golden-colored horse with yellow/gold hair, this one can be broken during a quest/mission that you do at Bonnie's ranch. When you go out to break horses with her and her father, she will tell you to break a golden-colored horse. That is the Kentucky Saddler. thanks to geegers78 for pointing out that after this mission the deed will be available but you may still need to break another saddler.

Hungarian Half-Bred - A white/grey-colored horse with a black nose, this one can typically be found in a plain to the east of Escalera. If you look on your map in-game, you'll see this plain marked with three running horses on it. You can also find them in the far east of Mexico, out by El Matadero and Casa Madrugada. Also, as pointed out by Jack Burton, you have to break a Hungarian Half-bred for the stranger task: Love is the Opiate. thank you.

American Standardbred - A completely black horse, this one can typically be found in a plain to the south of Beecher's Hope in West Elizabeth and occasionally in Tall Trees.

Again, these are the MOST COMMON places to find these horses. It does not mean they are the ONLY places. Rarely, you might find one of these horses accidentally mixed into the fold in New Austin or West Elizabeth. Credit goes to Jakob187 for the clarity.

In the event that the achievement does not pop upon breaking the last horse it is suggested you first check for the three specific horse deeds at any general store. If they are all there then simply go out horse hunting and break them all again and it should pop as CHEEZUS points out. You can't just buy the deeds, you have to break the horses.

This achievement is to break 3 different breeds of horses. First you need to get the lasso from mission "Wild Horses, Tamed Passions"... which is where you'll get the Kentucky Saddler. I believe it's the 3rd quest from Bonny. The Kentucky Saddler is golden pearl in color.

The American Standardbred are in the Great Plains and Tall Trees. This horse is lean and black in color. I found mine south of Beecher's Hope and Dixon's Crossing.

The Hungarian Half-bred’s are most commonly found in (and all over) Mexico. It's white in color with a black face. Look in in Nuevo Paraiso, Mexico (North East of Torquemada; or above "Coronas" of Diez Coronas on the map), usually found roaming alone, away from other herds.

A description of what each horse looks can be found at the local market seller and at the bottom of the list to buy it has horses, the bottom 3 are the rare ones which you have to find. Press Y for info.

Thanks @biggerballblat

To "Break" a horse, all you have to do is lasso them, hop on, and survive long enough to get them to stop bucking. Now, the Kentucky Saddler is story related, and you get one after doing the mission "Wild Horses, Tamed Passions." The American Standardbred is most often found in West Elizabeth (which is the Northern part of the map where Tall Trees and Blackwater are, for anyone who was wondering), and is a fully black horse (black maine and body). Finally, the Hungarian Half-bred is found in Diez Coronas in Nuevo Paraiso, and it is pure white, but with a dark muzzle. After you have broke these three horses, the achievement will unlock.
Cheers!

heiwaboke and mantrapolo have 2 very good, detailed solutions guides!

FYI: THIS ACHIEVEMENT HAS BEEN REPORTED AS GLITCHED. PLEASE READ THE COMMENT SECTION BELOW FOR FURTHER DETAILS BEFORE VOTING NEGATIVELY. Thanks!

it should also be noted, even though you break the kentucky saddler in the "tamed passions" mission with bonnie, YOU STILL NEED TO FINE ONE TO BREAK IN THE WILD in order to unlock this achv.

The kentucky saddler is golden/blonde pearl in color and can be found near new austin and east of macfarlane's ranch.

fyi, the kentucky's deed will be available to purchase in the store after you complete the mission so that's not a good method to checking off whether you have broke it or not. i suggest you find and break the kentucky again, from the wild, soon after finishing the 'tamed passions' mission so you know what you're looking for. ;)

msg me if you need any help: geegers78

Here is a visual representation on how to get this achievement. This achievement is not difficult at all but it may take you some time to get the horses by your lasso and "break" all 3 of them

All credit goes to Rooster Teeth.

Even though you break the Kentucky Saddler during the main story, you will have to find it and break it again in the wild. Often near Cholla Springs or East of Macfarlane's ranch, though I found mine near Rio Bravo.