Hi Natcha16.
The “Manual Adjustment” requirement for a badge referrs to the “Manual Adjustment” action you as an admin can do. When you manually adjust a users balance in the admin area (on the Users page), this adjustment is logged under the reference “Manual Adjustment”.
So if you want you can create a badge for users who had their balance manually adjusted x number of times or for x number of points. However, it has nothing to do with manual assignments of badges (which as Doremdou correctly pointed out is not supported).
Each time a user gains / loses points, this adjustment is logged under a unique reference. These references help us keep track of how and for what a user gained points and make it easy for us to for example add up all point gains for ie. “Logging in”.
These references is what you see in the dropdown menu when you add/edit a badge.
So as an example, when a user gains points for logging in to your website, the points are logged under the reference “logging_in” while when a user buys items in e.g. WooCommerce it is logged under the reference “woocommerce_payment”.