Hello Petronel,
the prices for the cog railway can be found here:
https://zugspitze.de/media/downloads/preise_zahnradbahn_sommer18_web.pdf
Unfortunately only in German. But there is an One-Way-Hiker ticket just up to the Riffelriss “Riffelriss Fußgängerkarte”. That’s 14€ for an adult person.
The corresponding timetable can be found here:
https://zugspitze.de/en/summer/news/oeffnungszeiten
The cog railway starts at the Eibsee, That’s the the same location where the German cable car up to the Zugspitze starts.
And as far as I remember there is either a shuttle bus or a train that you can use to travel between Hammersbach, the little village nearby the Höllentalklamm, and the Zugspitz station at the Eibsee.
Edit: Just found a nice activation report from @DL4ROB who did the route just the other way around:
73 Stephan, DM1LE