Hello!
Let's face it: this game is pretty boring to play alone and the achievement is downright ridiculous, so I've come up with a method to farm the achievements with the least amount of actual gameplay needed. For this we'll need Autohotkey and a little macro script I'll share with you. The script and the instructions are in the next sections.

Given how Unity works, the script CAN'T be running on the background, as the game will not receive our inputs if the windows isn't focused.
I recommend playing the game windowed for this method.

Open the game and go to the config in the main menu and be sure to set the player 1 control to Keyboard.
Now go to battle and change these settings:

• In Settings, Infinite stocks and 30 minute time limit or NO time limit.
  
• In EXTRA SETTINGS, up Game Speed to 2.
  
• In OTHER SETTINGS, set Knockback Multiplier up to 10.
  
• Also, turn Turbo Mode On. I don't really know if this is important but I enabled it.

Now, choose a character and pic another character (preferably a lighter one like the Blue Blob), and set it to controller 2. That's right, don't add bots. Just a 1 vs 1. Then, chose some flat terrain stage like Training.
You will have to pause the game and set the Game Speed to 2 again, because the settings menu doesn't seem to work.

Move your character next to the other one and enable the macro... And come after 30 minutes to start again.

In a 30 minute match with the Game Speed set to 2 (15 minutes real time), I got 251 kills.

That means that to reach 99.999 stocks at 250 stocks per game, well need about 400 games, 6000 minutes or 100 hours. Yikes!
At least we can do something else while this runs!

• Download AHK[autohotkey.com].
  
• Install it. Express install is enough. Then Exit.
  
• Create a txt file and paste the script. Change the extension to ahk make it so it opens with AHK. (Right click the script, Properties, "Open with" and press the "Change" button)
  
• Double click the ahk file.
  
• Press Control + J to start the script. Press Control + J again to stop sending inputs.
  
• Click the game so it gains focus so it receives the inputs.
  
• Right click the AHK icon in the tray and press "Exit" to close it when you are done.

Remember:

• Run - CONTROL + J
  
• Stop - CONTROL + J (may not work on first try)
  
• Exit - Right click AHK icon in the tray and EXIT.

Script for 30 minutes games:

Script endless games:

The script is a little bit wonky, let me know if there's something wrong, but I don't guarantee that it will work in your specific setup.

Mine was a Windows 10 x64 with the game windowed. It *should* work that way.