According to the Wiki it takes 250 seconds or 4 min 10 sec to break obsidian by hand.
(Technically that's not mining since the block is destroyed with no drops.)
Breaking blocks underwater takes 5 times as long, or 25 times as long if you aren't standing on the bottom.
So, 1250 seconds or 20 min 50 sec
Normal Level III Mining Fatigue from an Elder Guardian slows block breaking by 99.73%, which if I'm doing the math right means it takes 370 times as long (370.370370370... to be exact).
So 462962 sec or 7716 min or 128 hr 36 min or 5 days 8 hr 36 min.
(And multiply that by 5 if you are swimming rather than standing on the bottom.)