This description of the Enchantments (Alpine Lakes Wilderness, WA) from the Washington Trails Association (WTA) site provides an excellent overview:
In the Enchantments, nature has carved one of the magnificent places of this world--an alpine paradise of granite worn smooth by glaciers, larches manicured by wind and cold, and crystal blue lakes strung together by a creek that tumbles and thunders between them. Seemingly everywhere, herds of mountain goats calmly wander by. Superlatives simply don’t suffice, and you quickly find yourself resorting to otherworldly comparisons, just like the early visitors who bestowed place names like Aasgard, Sprite and Leprechaun on the fairy tale surroundings.
There are three ways to experience the Enchantments, none easy. The absolute minimum price of admission here is a hike of not less than seven miles gaining at least 4,400 feet in elevation in order to make it to even just one of the lakes in the Upper Enchantments. If you're lucky enough to get an overnight permit, you can backpack at your leisure via the Snow Lakes or Stuart Lake trailheads. If you’re a very strong hiker, you can make it in and out via either trailhead in a single day, although seeing all of the lakes this way is so grueling it borders on the impossible. With two cars (or a car and some bikes), you can hike point-to-point from one trailhead to the other and transit between the two. The thru-hike is typically done from the Stuart Lake trailhead, because it reduces the total elevation gain by 2,600 feet relative to going the opposite direction (although it still takes in the punishing climb up Aasgard Pass, which rises 1,900 feet in less than a mile). Pick your poison; enjoy the rewards.
My daughter and I did this transit on August 12, 2016. The description above might be a bit discouraging ("is so grueling it borders on the impossible") but we found this hike to be extremely enjoyable as a one day, with pain only nagging us at the end towards the Snow Lakes Trailhead. We availed ourselves of the Leavenworth Shuttle, allowing us to leave our vehicle at the Snow Lakes trailhead and begin our hike at the Lake Stuart trailhead, feet on the trail at 6:20 AM, well worth the price of admission. We were not in top shape for this but, knowing the score at the get go, our plan was to linger in the upper basins and endure the interminable downhill slog after Nada Lake. We snacked, soaked our feet in the cold waters, and at one point stood for twenty minutes as a mountain goat and her kid munched on grasses right up to our feet; we may as well have been trees or rocks. So awesome were the views that I snapped 450 pix along the way. This area certainly lives up to its reputation, and we found the crowds thin in the upper areas, possibly because the strenuous nature of this hike weeds out the casual backpacker. By upper areas I mean from Aasgard pass to Lake Viviane. Last year we had a core permit but the weather was daunting, drastically thinning out the usual summer throngs with reports of snow and 60 MPH winds. We certainly enjoyed our stay there but after exploring the area in rain and wind wearing 3 layers, this transit in incredible weather was indeed a visual and experiential feast, well worth the payment in grinding downhill and sore legs afterwards.