This achievement is super easy if you know what you're doing.
There are four rooms indicated at the bottom of your HUD. Simply follow the Bowler Hat Guy to whichever room he is in as he will appear in your HUD in the room he is in. (Use left and right triggers to switch between rooms).
Shoot him for points, then shoot the hats he throws out as quickly as you can. Tapping the shoot instead of holding the button makes the security system shoot faster. Once you've taken care of the hats, if you have time repair any damage by shooting whatever it was the hats destroyed. But mostly concentrate on destroying the hats and keeping up with the Bowler Hat Guy.
Continue this until you reach 100,000.
Note: As you progress in difficulty you'll receive multiplier bonuses. So don't worry it doesn't take as long as you might think.