Run in PhpMyAdmin:
DB="your_database_name" USER="your_db_user" PASS="your_db_pass" ( echo 'ALTERALTER DATABASE `'"$DB"'` CHARACTER SET utf8 COLLATE utf8_general_ci;' mysql -p$PASS -u $USER "$DB" -e "SHOW TABLES" --batch --skip-column-names \ | xargs -I{} echo 'ALTER TABLE `'{}'` CONVERT TOyourdatabasename CHARACTER SET utf8 COLLATE utf8_general_ci;' ) \ | mysql -p$PASS -u $USER "$DB" utf8_unicode_ci