I did Tyndall and Williamson in the 80s with a buddy. We got a shuttle ride to the trailhead late at night, hiked for maybe 3 hours with flashlights (no headlamps back then). Then camped overnight literally on the trail.
Day 2 we made it to Shepherd Pass. We were carrying 50+ lb packs, had planned on a week-long trip. We spent the night, I had AMS pretty bad.
Day 3, we did Tyndall, got done so early, we decided to move our packs down to Lake Helen of Troy (That took way longer than expected, it is rugged, even if it is dropping altitude) THEN we climbed Williamson that afternoon. I was ok at the end, but my partner dry-heaved several times.
That night at Lake Helen of Troy was the worst windy night ever. Couldn't sleep with the wind pounding the tent so badly, it was popping loudly most of the night.
Next morning (day 4), we were beaten (family issues too), canceled the rest of the trip (had planned on a Trojan, Barnard, Russell, Whitney x-country epic), and hiked ALL day to get back to the trailhead. No car, so then hiked out to the Onion Valley road, where we hitched a ride back to Independence, paid for another shuttle back to our car at Whitney Portal. 'Twas the craziest hike of my life!
Bottom line: Once at Shepherd Pass, you CAN do both peaks in a day. But you have to have the mindset to do it.
