Depends on the damage cap. If it's 9999, it'll be very long. 200 million divided by 9999 is 20003 hits. Time invested is 60 seconds in a minute, 60 minutes in an hour, 3600 seconds. Assuming you can do 9999 per second (not bloody likely), 20003/3600 is 5.556 hours. Account for preparation and healing periods, that is a six or seven hour battle. Eight if you suck or strike the unlucky bar on the in-game randomizer.

If the cap is 99999, then 2001 hits. Less than an hour.

Sounds like a lark.