You will find 3 references on the net by individuals who have hiked all the way to the "back wall." All 3 references were from trips over 5 years ago when the route was flagged. The flags have been removed since the "Ultimate Guide to Kauai" was updated in 2008 to include the first half of the route from the end of the road to the convergence waterfall about 2 miles upstream.
Beyond the convergence waterfall, the route is no longer marked, which means THIS IS NOT A DAY HIKE. The route is incredibly dangerous, overgrown, with lots of exposure in certain spots. You can't make it all the way in a single day unless you know exactly where to go. So if you're determined to do this hike, you need to plan for an overnight bivouac (hammock and rainfly only...there's no space for a tent anywhere along the hike).
Incredibly strong hikers (and I'm talking people who can do Half Dome round trip in a day...ie 20 plus miles, with LOTS of elevation gain and loss) can expect to reach the back wall in 6-8 hours one way from the trailhead if you manage to find the way...but this is not likely now that the flags have been removed.
Instead of attempting to go all the way, I recommend you just boulder-hop upstream from the end of the road to the convergence waterfall, which takes about an hour and a half each way, and is a fabulous destination. Great waterfall views, lots of places right around the waterfall to explore, and leave it at that. This is an incredibly risky hike to attempt in a single day. DO NOT hike after sunset, as the risk for broken ankles or legs is extremely high. The moss-covered rocks in and along the Wailua River are the slickest you'll find anywhere in the world.