First do

ALTER DATABASE database_name CHARACTER SET "utf8";
ALTER DATABASE database_name COLLATE "utf8_unicode_ci";

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After that, for each table:

ALTER TABLE table_name DEFAULT CHARACTER SET "utf8" COLLATE "utf8_unicode_ci";

This just changes the default character set / collation for each table. To convert them, you need:

ALTER TABLE tablename CONVERT TO CHARACTER SET utf8 COLLATE utf8_general_ci;