Here is a link that outlines how to write good acceptance criteria. Some highlights:
Each acceptance criterion is independently testable.
Acceptance criteria must have a clear Pass / Fail result.
It focuses on the end result – What. Not the solution approach – How.
Include functional as well as non-functional criteria – as needed.
Team members write ...
Can you help me understanding how can I verify/validate the system like I used to in the previous approach?
Agile does not mean vague. Quite frankly, you are right. Those acceptance criteria you have problems with are just bad. That has nothing to do with agile of any kind. Acceptance criteria should be testable. If you as a QA person do not know how to ...