framing a basement wall under a steel I-beam

The most effective and common method, although the one that probably takes the most elbow grease, is to drill a few 7/16" holes up through the bottom flange of the steel beam on one side for 3/8" bolts with nuts and washers. Don't try to center your top plate, you'll end up drilling through the thickest part of the flange. Make one edge of your top plate flush with one outside edge of the flange. With this method, a non-load bearing wall can be attached to the beam with only a few holes...like 3-4 feet on center.

I'd say that for this wall, the best method would be either powder actuated fasteners or simple PLPremium glue with and overnight clamp job. Either one would be faster and easier than all that overhead drilling.

Drilling might require a bit more up front work, but it will definitely provide the sturdiest, most long-lasting wall. Cutting corners isn't worth the 30 minutes you'll save.