I will warn you upfront that this is very tedious and should take roughly 13-16 hours of pure grinding even under the best conditions, depending upon how many kills you already got thorough your play-through.
You will want to attempt this when you get access to the Ragnarok at the earliest, but you can attempt it as late as regaining the Ragnarok on Disc 4 if you wish. If you are doing the Contrived Finish achievement, I recommend you make a save on Disc 4 just before confronting Ultimecia and get that achievement and then come back for this bad boy once you've completed the game.
Your party will consist of Squall, Selphie, and a third member of your choice. I recommend whomever has the most impressive Strength. I don't recommend Rinoa because her attack animation is stupidly long. You can't have Squall leave the party here and he will earn experience, so this is why I recommended you finished the Contrived Finish achievement first. Squall and Selphie with her ultimate weapon have 255% Hit, which means it is guaranteed. You will need at least 67 Triple spells to junction to Hit to reach 200% on your third character, maybe a little less depending on the Hit of their weapon. This is important.
A good Strength Junction is also important for all members. Ultima is ideal, granting 100 Strength at 100, but farming 300 can be painful. 100 Meteors is your next best option, granting 75 Strength. Give all three characters the Initiative ability, and one the Alert ability. At least one character needs to be fast as possible to mop up a potential fourth enemy after the initiative turns. 100 Triples to Speed on Squall or Selphie is ideal but Haste only gives 10 less. You will also want to refine the Kiros card into Accelerators for Auto Haste. You can get copies of him easily from the CC group on the Ragnarok even if you didn't do the Queen of Cards quest. But you did need to defeat the CC group.
Now that the prep is done, let's get down to business. You will be killing tons of Cactuars on Cactuar Island. This is the most target dense encounter area in the game, and they can be reliably hit and one-shot if your characters are adequately prepared. By running around on the sandy area of the island, you will encounter two or three Cactuars at about an equal rate, and more rarely encounter four. You will never encounter just one. AVOID the rocky areas of the island. There you will encounter one to three Cactuars instead. I found it is best to park the Ragnarok on the southern-most tip of the island and run directly across the sand to near the northern most tip where the sand begins ending, back and forth.
Cactuars are fast, and have 100 Evasion at all levels. But with 200% hit, you are guaranteed to hit. They have absurd Spirit, so they take almost no damage from magical attacks, but they have very mediocre HP and Vitality stats. You can just hold down the X/Confirm button during battle and they should be one-shot by your physical attacks. You can use the Strength+20/40% etc abilities if you need them as well. Your fast character may not be fast enough to mop up the fourth one before it escapes or attacks because the ATB the Cactuar gets at the start of battle is random, but it is mostly reliable.
They also drop Cactus Thorns, which can be refined into Hundred Needles with Eden's GF-Abl Med, and Hundred Needles can be refined into a Spd Up with Doomtrain's Forbid Med RF, so you're actually doing something kind of productive to max out your characters other than just getting this achievement.
Assuming you use the game's built-in Turbo function on F1 (which you may or may not consider cheating) you should go from the Overworld to the screen tear for an encounter in about 3 seconds on average, and it should take about 12 seconds to actually complete the average encounter from screen tear all the way back to the Overworld. So each encounter "cycle" takes about 15 seconds. Based on the odds of the 2 to 4 Cactuar encounters you should encounter an average of about 2.65 Cactuars a battle. That's about 636 dead Cactuars an hour. To kill 10000 would take you about a quarter of an hour shy of 16 hours total. If you refuse to use Turbo, this could easily take twice or three times as long.
I don't recommend you do this all in one sitting, and do recommend you have some outside entertainment but there's the rough math. I figured this out by recording my own play and taking notes. Good luck. This is the most grindtastic achievement in a Final Fantasy, worse than even Perfect Sphere Master and appears to be worse than FFIX's identical achievement due to the slightly slower pacing.