You don't have to use eval to get the keys of the package's symbol table, just do
in reply to Listing the functions of a package / methods of an object
no strict 'refs';
my $st = $class . '::';
@subs = keys %$st;
Unfortunately, there's no way to differentiate between methods and regular subroutines, and as moritz pointed out, that won't find inherited methods which exist in different packages. Moose's metaclass facilities are really great, but naturally they only work for objects that are built with Moose.
There is Class::Inspector, which has a reasonably good function to search a class's @ISA tree and get a list of every possible inherited method.