Like so?

#!/usr/bin/perl

# http://perlmonks.org/?node_id=1184431

use strict;
use warnings;

for ( split /^BEGIN_TAG\nX\d+ /m, do { local $/; <DATA> } )
  {
  s/\n */ /g;  # combine lines
  s/ X\d+/;/g; # change Xn to ;
  s/\s*\z/\n/; # make sure \n at end of line
  print;
  }

__DATA__
BEGIN_TAG
X1 test test test
X2 no no no no
X3 yes yes yes
BEGIN_TAG
X1 test test test
tes test test
X2 no no no no no
nono non no no
 nononono no no  no
X3 hi hi hi hi hi hi
hi hi hi hi
hi hi
[download]

ignoring what seems to be a typo in the output you show.