You need to use JavaScript or something to archive this. This can not be done using plain HTML.
The following code worked for me. Hope it will be helpful.
<ul>
<li><input name="check[]" type="checkbox" value="check 1" required><label>check 1</label></li>
<li><input name="check[]" type="checkbox" value="check 2" required><label>check 2</label></li>
<li><input name="check[]" type="checkbox" value="check 3" required><label>check 3</label></li>
<li><input name="check[]" type="checkbox" value="check 4" required><label>check 4</label></li>
</ul>
<input type="submit" value="Check" id="check">
jQuery code,
<script type="text/javascript">
$(document).ready(function () {
$('#check').click(function(e) {
var ischecked = $("input[type=checkbox]:checked").length;
if(!ischecked) {
alert("Please select at least one checkbox.");
return false;
}
});
});
</script>