As you aready know, you go into the teleporter, make your way up to the highest ledge and flip the switch. It will raise a small platform in the middle of the toxic lake. Run down and press the "Use" button. It will rise, and hopefully with you on it. Pull out your rocket launcher. Now, the next step requires a lot of skill and planning and good eyesight and judgement. When the nose of your launcher is pointed at the chin of the goat's head, FIRE!! Hopefully, the rocket will go down the gole in the beast's forehead and you will hear a scream. Repeat as necessary. You should only have to do this twice, if it works both times.
Here's an even simpler solution. While you're in the room with all the ammo and weapons, type "idclip" and run straight through the wall, past the ledge, and into the boss's head. You will see John Romero's head in there. (He's a creator at id Software.) All you must do is shoot the head as many times as needed. Just use the BFG.