There are 2 Inside track betting shops in the game that I know of, however the one I am going to be referring to is the one in Downtown Los Santos shown in the image in another guide for this achievement.
Now, if you do it this way you will get both this achievement, and a whole load of money.
You can do this as early as you want, but I personally waited until I had about $160,000 in my pocket to spend (it took me a lot of missions to get that amount and I hardly spent anything other than to buy the airfield in Las Venturas.)
When you have the money needed, find the green house on the map in Los Santos for the area named Jefferson (it is next to Glen Park which is the area you had your gang territory fight training in and is also underneath the northern most clothing shop in LS) buy the house for $10,000 and
save the game. Due to its close proximity to the betting shop it will be our little hub. Now go all the way to the betting shop and place all your remaining money on the Teal horse which is the 12/1 betting odds.
Watch the race, and if you win you will need to go back to the Jefferson house and save the game again, and repeat this as many times as you wish; if you lost, just reload your save that you made and try the same tactic again until you win as it is just luck whether you win or not. Due to the Definitive edition being a lot quicker, loading will not take too long and this tactic apparently shouldn't take any more than 4/5 reloads at most to get a win (I personally got 2 wins on the trot and it set me up with $23,000,000)
That is all folks, and it is how I got the achievement plus my millions in order to buy everything in the game.
If anything is off with this guide guys just let me know. Happy Hunting