Max,
Last year my husband and I were looking for a good hike in the Garmisch area. I found an old post of Lola's that was about the hike she mentioned above. DO IT! It is a great hike. My journal shows we were on the trail at 12:20 (We had to pick up a rental car and drive down that morning from Munich) It took us about an hour to reach the entrance of Hollentalklamm. Going through the gorge is beautiful and gives this hike a unique experience. We hiked onto the hut from there. Because of our late start, we didn't stop to eat (however, we hiked back up to the hut to eat the next day...it's that great). We pressed on. You actually have 2 options. You can go up to the Alpspistze and ride down or you can hike over to Kreuzeckhaus and ride a lift down. (The lifts are side by side when you get down.) Because the Alpspitze is higher, it had a cloud sitting in the top. So we stayed lower (which had great views) and went to the other hut and rode down. My journal shows we arrived at that hut about 4:20. So it was about 4 hours of continuous hiking. (We are 63, avid hikers and used to elevation gains, so some people may do it slower than us and some faster than us.) The Hollentallenger hutte was about 1/2 way.
We stayed in the little town of Grainau. It is our favorite town in this area. All the hotels give you a Grainau pass that allows you to ride to the train and buses for free. If it is a day trip, and you plan to go back to Munich, there is a pay parking lot right at the base of the start. When you reach the bottom of the lift, you have about a 7/10 of a mile walk back to the parking lot. If you take the train down, you can ride the smaller train over the base of the lifts and walk over to the start of the hike. It starts in the Hammersbach area. The trail to Hammersbach is not obvious, but you just start making your way that direction and it works. The day we were there, many people were walking between the two.
I highly recommend this hike. Let me know if you need more info. We did get the brochure on Hollentalklamm at the visitor's center Here are some web sites about the hike (and you can do it going the other direction where you ride up and hike down. I prefer hiking up as coming down is hard on the knees)
https://www.outdooractive.com/en/route/mountain-hike/zugspitz-region/from-mount-kreuzeck-through-the-hoellental-hoellentalklamm-/1397829/
This one describes the hike to the higher up hutte. We saw the small trail it describes. From the Schwarzekopf, you can make your way down to the Alpenspitze. (haven't done it myself though)
https://www.summitpost.org/hammersbach-and-via-the-h-llentalklamm/244007
This one describes the other route:
https://hikingmadness.wordpress.com/2015/06/22/alpine-scenery-and-hoellentalklamm-gorge/
And a video (done the opposite direction we did and going to Alspitze) It does give you an idea of the incredible scenery. At the end, you can see how she is walking along the train tracks back to the bottom of the lift.
https://www.youtube.com/watch?v=cDMjiVmV4KE
I hope this all helps. I spent a lot of time researching hikes for our trip last September, and this one lived up to expectations.