Here's an example of dumping the slice overlapping the human BRCA2 gene in EMBL format:

use strict;
use warnings;

use Bio::EnsEMBL::Registry;
use Bio::EnsEMBL::Utils::SeqDumper;

my $registry = 'Bio::EnsEMBL::Registry';

$registry->load_registry_from_db( '-host' => 'ensembldb.ensembl.org',
                                  '-port' => '5306',
                                  '-user' => 'anonymous',
                                  '-db_version' => 63 );

my $sa = $registry->get_adaptor( 'Human', 'Core', 'Slice' );

# Get slice overlapping BRCA2 gene:
my $slice =
  $sa->fetch_by_region( 'Chromosome', '13', 32889611, 32973805 );

my $seqdumper = Bio::EnsEMBL::Utils::SeqDumper->new();

# Disable uninteresting feature types:
$seqdumper->disable_feature_type('estgene');
$seqdumper->disable_feature_type('genscan');
$seqdumper->disable_feature_type('repeat');
$seqdumper->disable_feature_type('similarity');
$seqdumper->disable_feature_type('variation');
$seqdumper->disable_feature_type('vegagene');

# Dump to stdout:
$seqdumper->dump( $slice, 'EMBL' );

Cheers, Andreas (Ensembl/Core)

The EMBL format dumps for Ensembl are here: ftp://ftp.ensembl.org/pub/current_embl/homo_sapiens/README

Why do you need to do this via the Ensembl API? Files like these are available for downloaded from EMBL-bank directly at: http://www.ebi.ac.uk/genomes/eukaryota.html

e.g. chromosome 22 in version GRCh37 can be downloaded in EMBL format here (n.b. this is a 10 Mb file)

Using the Ensembl API, there is a module called Bio::EnsEMBL::Utils::SeqDumper which, if given a whole chromosome Slice object, can write this data out.

Do you need more explanations/more complete script- just ask.