You will need
Turbo (at least one syringe, though two are recommended)
Spiked/Brass Knuckles
Speech of 60

How to Obtain the Supplies
Turbo can be bought from various shopkeepers or looted off raiders

Mr. Holdout sells both Spiked and Brass Knuckles, though Spiked Knuckles can be found in a Boulder City house if you don't feel like spending the caps.

A Speech of 60 can easily be reached by a character with a Speech of 30 or 40. This can be done multiple ways
If you have a Speech of 40, wearing Naughty Nightwear (+10 speech, purchasable from Mick in Freeside) and using a Meeting People magazine (+10 speech)
You can also take the Comprehension perk to double the bonus from skill magazines, making it so a character with a Speech of 30 could reach Speech of 60.

Step 1: Speak to Benny and pass the Speech check, causing him to go the Presidential Suite alone
Step 2: Equip your Spiked or Brass Knuckles
Step 3: Speak to Benny, but don't attack him through dialogue. Wait until he gets up to leave the suite.
Step 4: Punch Benny once. When he draws his gun, use the turbo and start hitting his gun until it falls.
Step 5: Pick up the fallen pistol and equip it.
Step 6: Kill Benny with it.
Step 7: Congratulations! You should now have slain Benny with his own pistol and completed the challenge.

Reminder: Make sure you have had no console commands activated during your current session, or this may not count towards the "Combat Veteran" achievement.

Well, you have now slain Benny with Maria, and made him feel the pain you felt in the Goodsprings Cemetery. Now, just take off his suit, get the Pompadour haircut (obtainable from Sergio in the Kings), and you can become Benny!