*note*
The 3rd time i met the bullish man was in a room where you are NOT meant to kill him but TRAP him behind the roller door which closes when you press the button to release him.
*solution*
once you have pressed the button on the wall to release him from his door press the button agian to open the roller door which had closed, (to the left of the button) then get him to chase you in there then running out again and pressing the button again to lock him in there.
Bullish man gone!
*bonus*
Once you have trapped the bullish man behind the door, open the roller door agian by pressing the button and go through the doors and you will find a billy puppet. combo for the door i used was 780.
Then the next time you meet the bullish man use the above solution for your cheevo.
Hope this helps