As with all PADI courses, the PADI AOWD dives have specific theoretical and practical performance requirements which must be met in order to 'pass' the dive (and hence gain the AOWD rating). These performance requirements can only be assessed and verified -- and the dive signed off as complete -- by a PADI instructor who is in 'teaching status' for the current year (i.e. they have paid their annual membership fees, are receiving standards updates, and are not currently suspended for standards violations).
While the theoretical component can largely be completed in your own time, and is minimal compared to the OWD course (consisting simply of reading the relevant five chapters in the AOWD manual, and completing the Knowledge Reviews), your answers to the KR must still be reviewed/signed off by a teaching-status PADI Assistant Instructor (AI) or better.
Although the training dives do not all have to be conducted by a single instructor/company, a PADI Open Water Scuba Instructor (OWSI) or better MUST be present at the dive site and monitoring each training dive, so that s/he can correctly explain the dive performance requirements, and verify (either directly or indirectly) that they have been successfully completed. The PADI standards do not require the instructor to accompany the student on all the dives: for the Navigation and most of the elective dives, the student(s) may be accompanied in-water by a PADI Divemaster/AI, or even just their buddy, with the OWSI+ providing surface cover and monitoring the buddy pair's progress and position (via their bubbles, or an SMB).
(That said, I believe that UK H&S legislation requires that all training dives conducted in UK waters be supervised in-water by at least one certified diver with 'dive leadership' skills -- not sure if/how that applies to diving with your Uni club in Cyprus).
PADI make at least one exception to the above rule: the (obligatory) Deep Dive MUST be directly supervised in-water by a PADI OWSI+. I believe the AOWD Wreck Dive must also be directly supervised by an instructor (and even if not, this would still be a good idea if you're hoping to do it on the Zenobia!). As such, you could not simply do a deep (>18 m) or wreck dive, bring your logbook to a dive centre, and expect them to sign it off as one of your AOWD dives (according to PADI standards, anyway).
Caveat:
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Ideally, and if the dive centre/instructor is following PADI standards, this should also be true for every dive you do for the AOWD rating. An AOWD training dive should be planned and executed as such from the start: a random drysuit / night / multilevel / photography dive should not be signed off 'ex post facto' as an AOWD dive. While you may well be able to find instructors in Cyprus who are willing to do this for the price of a pint (or less!), they will be breaking standards, and you will not get the full benefit of the AOWD course/rating. Doing so will leave you 'certified' without actually being 'skilled' -- and while you may not care about this right now, you will likely regret it later.
For example, learning to navigate large/complex patterns successfully during your AOWD dives (e.g. the AOWD Navigation, Search+Recovery, and/or Night dives -- if these are taught properly!) will make ALL your subsequent dives much easier. Not only is this an absolutely essential skill for diving in low-vis (UK) waters, but if and when you decide to do your PADI Rescue Diver or BSAC Sport Diver/Dive Leader course, you will be expected to (be able to) navigate underwater search patterns accurately, using both a compass and natural cues. If you skipped learning these skills, you would be cheating yourself.