A fairly standard approach is to break the identifier up into a letter part and a number part, sort by each as needed, then join the bits back together again. There is a Perl idiom that makes that fairly easy and clean to do:

use strict;
use warnings;

my @rawList = qw(
    CORE1
    COREA11
    CORE12
    COREA130
    CORE8
    CORE233
    COREA12
    COREA115
);

my @sortedList =
    # Join letter and number parts back together
    map{$_->[0] . $_->[1]}
    # sort first by letter part, then if that is equal sort by number 
+part
    sort {$a->[0] cmp $b->[0] || $a->[1] <=> $b->[1]}
    # Use a regex to split each item into a letter part and a number p
+art
    map{[/([^\d]+)([\d]+)/]} @rawList; 

print join "\n", @sortedList;
[download]

Prints:

CORE1
CORE8
CORE12
CORE233
COREA11
COREA12
COREA115
COREA130
[download]

Note that map takes a list, processes each element, and returns a new list. The expression executes its main parts essentially from right to left: the last map executes first, then the sort, then finally the first map.