A few sections require a little more detail:
-There is an abundance of trails between Lake Lillian and Rampart Lakes, none of which are official or maintained. I've highlighted one possible option but you'll find several other trails branching off of and rejoining your path. As long as you're heading generally north and not losing too much elevation, you're going in the right direction.
-Traces of very old trail and the occasional cairn mark the way between the tarns below Alta Mountain and Chikamin Pass but overall it's effectively cross-country travel. The faint trail that climbs to Box Ridge is visible on the slopes east of the tarns below Alta and several of its switchbacks are hard to miss higher up. Once on the north side of Box Ridge, the trail starts out strong but then disappears quickly. I recommend continuing north towards Chikamin Pass, staying above treeline and traveling across talus fields, for the easiest route but it's also possible to drop to Park Lakes (through heavy brush) or stay high along the ridge (with much more scrambling and exposure).
There are two alternate ways to finish this loop:
1. Exit via Joe Lake and the Gold Creek valley. It's a bit of a rough descent down to Gold Creek but this route will save you from some road miles. See Joe Lake Loop for more info
2. Exit via Kendall Peak Lakes. A short section of cross-country will connect the PCT south of Kendall Peak with Kendall Peak Lakes, where a good trail will take you back to Forest Road 4832. I haven't done this route yet myself so I won't describe it further, but it should be a relatively straightforward piece of cross-country to make it possible.
Distance: 30-ish including the road, 22-ish if you shuttle between trailheads
Elevation Gain: 9,700'-or-so for the full loop, about 1,000' less if you do a shuttle
Maps and More:
A few trip reports describing the Alta Mountain-to-Chikamin Pass section: