He made it to, what, 7 minutes-plus?
Assuming an 18 Con, acc. to the DMG...
- He could automatically hold his breath for 36 rounds (3 minutes, 36 seconds)
- From that point forward, he starts making Con checks, starting at DC 10, and increasing by 1 for each round.
- Assuming he made it to 7 minutes, that's a total of 34 Con checks, with the last one being at DC 43.
However...assuming no magical assistance or weird Action Point stuff, in order to even have a chance of making a DC 43 Con check (i.e., on a 20), he'd need to have a Con score of 54! And, if his Con were 54, he wouldn't even need to start making Con checks until after holding his breath for 108 rounds (10 minutes, 48 seconds).
So...by the RAW...his Con is somewhere above 18.