If you have SSH access back to your client (i.e. you're SSHing to one server then to another) and can thus scp a file back then this might work:
wget --save-cookies cookies.txt \
Then another Wget:
wget --load-cookies cookies.txt \
--post-data 'username=admin&password=[ADMINPASSWORD]' \
This is based on a StackOverflow post and works in two steps because the first request for /admin/environment.php needs you to be a site admin and you're not logged in so it sets the session variable wantsurl to the requested page and redirects you to the login page. The second step sends credentials to the login page but includes the session cookie from the first response so the login page sees the wantsurl value and redirects you there. Wget responds to this redirect saving the resulting page to environment.html.
This depends on the server you run this on being able to resolve the site domain name and access itself on port 443 or 80.
Possibly a bit messier than you were hoping but it seems to work.