In addition to the above, I’ll also just note that 批判 is kind of the all-purpose “This is being widely criticized” word, in terms of public backlash or reproach. Appears often in news and on Japanese Twitter.
批評 is for criticism in a more academic sense (though less academic than 評論, which would be like the equivalent of writing a humanities paper about the subject). Would be used for things like media reviews. This nuance seems pretty natural if you think about 評 on its own, indicating “evaluation.” Much like 評論, you’re examining points holistically and relatively constructively, but at the end there’s still an aspect of attaching personal positives or negatives to the subject. A critique.
And then if you can remember that the other two are more personal, in terms of their criticism (and less frequently used), you should be set.
EDIT – Meant to respond to the thread, not to Leebo directly. Sorry!
Edit edit – Quick distillation/closest translations:
批判: Criticism (general; backlash; used toward ideas, policies, and occasionally individuals)
批評: Critique; review
評論: Critical examination (academic; critical theory)
非難: Criticism (personal)