Since MySQL 5.5+, there is support for 4 byte characters. JIRA is capable of handling these characters when using other databases. Due to some limitations in how MySQL is implemented, JIRA won't just work by setting the 4 byte encoding utf8mb4. MySQL's InnoDB engine is limited to a maximum size of 767 bytes for any field used in an index, and there are various places in JIRA that use a VARCHAR(255) field in an index. This means that JIRA will encounter an error such as the below if you try to simply install into an utf8mb4 database:
A full list of InnoDB restrictions including this one is listed at http://dev.mysql.com/doc/refman/5.6/en/innodb-restrictions.html
You can use another database - PostgreSQL is an alternative which is also free. Alternatively if you are just having problems parsing an XML backup, then you could process the data manually and remove any 4 byte characters before importing to avoid the problem.