Once you can nail down the text that has the date in it, Time::Piece can do everything else.

#!/usr/bin/env perl
use strict;
use warnings;
use Time::Piece;

my @dates;

while (<DATA>) {
   next unless /Launching the JVM with following options/;
   my ($date, $line) = split /::/,$_,2;
   $date = Time::Piece->strptime($date, "----- %a %b %d %T %Y");
   push @dates, [ $date, $line ];
}

for (@dates) {
   print $_->[0]->strftime("%Y-%m-%d %T") . " $_->[1]";
}


__DATA__
----- Sun Mar 8 10:51:20 2015::4426::Launching the JVM with following 
+options.
# 2015-03-08 10:51:20 4426::Launching the JVM with following options.
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Change for to while while reading (<DATA>).. so you don't read all into memory at once