You can use mysqldump to make a backup of your database. Make another copy of it to be able to play safely and then use iconv to transform the backup.sql file from latin1 (that is iso-8859-1 i think) to utf-8.
iconv -f iso-8859-1 -t utf8 backup.sql > backup-iconv.sql
Drop the database and restore it using the modified .sql.
You can find more details here