How to get backup details for a particular client in gui

Go to Media > Save Sets and fill out the appropriate parameters in the mask (especially Client Name & Save Time).

Finally click the tab Save Set List to start the query ans verify the result

Didn't you use the Help option from either NW NMC or NWUI? Or the NW pdf documents?

For more recent NW versions, one can look at online resources without needing to sift through the whole PDF.

For nw19.8 that is (but would be similar for earlier versions also) specifically:
https://www.dell.com/support/manuals/en-us/networker/nw_p_nwadmin_19.8/searching-for-save-sets?guid=guid-b568920e-ed1c-4674-b214-973876062f7a&lang=en-us

Or do you mean other kinda overviews for the backups from a client?

I myself however prefer CLI using mminfo above creating overviews with NW NMC (but it has export options for example to save it to csv or pdf).