You're pretty close:

use strict;
use warnings;
my @lines;
foreach my $file ( reverse @ARGV ) {
    open my $fh, '<', $file or die "Bleah: $!";
    my( @slurp ) = <$fh>;
    push @lines, reverse @slurp;
    close $fh;
}

print foreach @lines;
[download]

This could be done with a lot more memory efficiency (without slurping the files) if you take steps to read the file in backwards in the first place (using File::ReadBackwards or Tie::File). But I kept it to stuff that you would probably find explained in the Llama book.

You usually automagically open the contents of @ARGV with the bare <> operator. Since I wanted to treat the files in reverse order, I didn't use <>'s magic, and instead opened the files explicitly. Actually that step could have been avoided if I had reversed the contents of @ARGV first, and then still relied upon <> to do its magic.

UPDATE: I wanted to go ahead and show how it is simplified by letting <> do its magic. Here goes:

use strict;
use warnings;

my @lines;
@ARGV = reverse @ARGV;
foreach ( @ARGV ) {
    my( @slurp ) = <>;
    push @lines, reverse @slurp;
}

print foreach @lines;
[download]

Enjoy!