Richard Kresser posted the route:
The Tatoosh Traverse consists of summitting 12 peaks of the Tatoosh Range, situated just south of Mount Rainier. One additional peak, ironically the namesake of the Range, Tatoosh, lies geographically separate from the other 12 main peaks, and outside the Park boundaries. Tatoosh is not a generally accepted peak within the Tatoosh Traverse, nor are a variety of sub-summit towers such as West Unicorn Peak. The accepted "Tatoosh Traverse" route is Eagle, Chutla, Wahpenayo, Lane, Denman, Plummer, Pinnacle, The Castle, Foss, Unicorn, Boundary (also named Border on some maps), and Stevens. Besides the initial trails out of the trailhead, the route is not defined by a trail and is a collection of climbers trail, scrambling, and technical climbing. You are allowed to go for the peaks in any order you desire, starting from whichever side you desire. Generally, the two trailheads are Snow Lake on the east end and Eagle Peak on the west end. To make it more pure, you must return by foot to your vehicle via the Wonderland Trail (additional 7.5 miles).
summitpost.org has more info: http://www.summitpost.org/tatoosh-traverse/156580