My in-game clock says 3:50, but my Wii clock says 6:10.
That involved 2 continues and some exploring in the earlier stages, and then just turning on the multiplayer for 2-3 minutes to see how it worked.
I think the more you die, the faster your time will actually be. If you have a 25 minute run, and die on the boss and use a continue, you could probably do a 10 minute run and then win.