This is a Premier Route. To claim an FKT on this route, you must meet a high standard of documentation and verification. See details here: https://fastestknowntime.com/premier-routes.

corsica.forhikers.com calls the GR20 "the toughest long distance trail in Europe". It runs about 180 km along the spine of Corsica.

Max Keith reported running this point-to-point route of 28km, with an elevation gain of 2800m, in 5h45m45s on 22 Dec. 2013. The route is just outside of Santiago, Chile, and begins at Ñilhue Bridge, Park Mahuida, and reaches the summits of Cerro Provincia, Tambor, San Ramon, and La Cruz. Keith appears to have had some support from a friend along the way. Here are is a report on the run, and a GPS track:

trailchile.cl/4-peaks-por-max-keith/

On May 31st 2014 I completed a solo loop around Rapa Nui (or Easter Island): 65.05 kms, 9hrs 5mins. And I think it stands as 'unsupported' - unless you count the little black dog who accompanied me for about 20miles - and the 2 glasses of rainwater I gratefully accepted along the way!! 

PHOTO 1: View of the southern coast of Rapa Nui and the site 'Tongariki' - in the middle of the pic is the crater of Rano Raraku (moai carving centre) - and also, in the foreground, my canine companion. 

This site has some info: https://besthike.com/s-america/patagonian-andes/cerro-castillo/

The 130km Huayhuash Circuit circumnavigates Peru's Cordillera Huayhuash. It is widely considered to be one of the top treks in the world. It includes numerous passes over 15,000' and up to 16,500'.