How to change attribute dropdown type to multi-select in Magento 2?

Short Answer:

Not possible via Magento2 Admin Backend.

Solution:

You need to update eav_attribute table and edit information about backend_source, frontend_input etc.

Simple query for that is:

UPDATE `eav_attribute` SET `backend_model`="Magento\\\Eav\\\Model\\\Entity\\\Attribute\\\Backend\\\ArrayBackend", `backend_type`="varchar", `frontend_input`="multiselect", `source_model`=NULL WHERE `attribute_id`=YOUR_ATTRIBUTE_ID_INTEGER LIMIT 1

Replace YOUR_ATTRIBUTE_ID_INTEGER with your attribute_id like 355

Reference:

https://stackoverflow.com/a/57701845/2229148