package Eagle;
@ISA = qw(Bird);

sub handler ($$) {
    my($class, $r) = @_;
    ...;
}

Starting with Perl Version 5.6, you can use subroutine attributes, and that's what mod_perl 2.0 does instead of conventional prototypes:

package Eagle;
@ISA = qw(Bird);

sub handler : method {
    my($class, $r) = @_;
    ...;
}

See the attributes manpage.

mod_perl 2.0 doesn't support the ($$) prototypes, mainly because several callbacks in 2.0 have more arguments than $r, so the ($$) prototype doesn't make sense any more. Therefore, if you want your code to work with both mod_perl generations, you should use the subroutine attributes.