The earliest you can get the Rocket Launcher is in DOOM II's MAP01: Entryway.
To get the rocket launcher:
From the start of the level up to where you enter a room where the exit door is. Take the elevator on the right and ride it up to the top. Drop down from it and land on the raised light platform. It will open a secret area back in the hallway. Return to the hallway and look to your right where all the health bonuses are, and you'll see the secret area opened where the rocket launcher is.
The best chance at the achievement:
DOOM II's MAP02: Underhalls has you facing three zombie infantry from across the river. Your chance of gibbing them all from hitting the one in the center is pretty high from this point, and only varies depending on the enemies' movements and how effective the rocket on contact and its explosion is. Save and load your game for repeated attempts until you succeed.