Backup your Magento code, database before upgrading.
In case of customization, you should backup the customized files and modify in newer version.
Now you remove app/code/Mageplaza/AjaxLayer
folder. In this step, you can copy override AjaxLayer folder but this may cause of compilation issue. That why you should remove it.
Upload new version Upload this package to Magento root directory
Run command line:
php bin/magento setup:upgrade
php bin/magento setup:static-content:deploy
Mageplaza_Core has been already defined
A: Read solution: https://github.com/mageplaza/module-core/issues/3
A: Please follow this guide: https://www.mageplaza.com/blog/magento-site-down.html