1. SSH into the Apple TV.
2. Use curl to download these two debs. You will have to pass the `--insecure flag`:
https://archive.debian.org/debian/pool/main/c/curl/libcurl3-gnutls_7.38.0-4+deb8u11_i386.deb
https://archive.debian.org/debian/pool/main/a/apt/apt-transport-https_1.0.9.8.4_i386.deb
3. Use dpkg to install the two debs, installing libcurl3-gnutls first.
4. Open sources.list in nano and add make the following changes:
a. Add these lines to the end:
deb [trusted=yes] http://archive.debian.org/debian/ jessie main
deb-src [trusted=yes] http://archive.debian.org/debian/ jessie main
b. Remove these lines:
deb http://ftp.debian.org/debian jessie main
deb-src http://ftp.debian.org/debian/ jessie main
deb http://security.debian.org/ jessie/updates main contrib non-free
5. Run the command `apt-get update`. It will take a bit, but then apt will function again.