There is a pdf of the report, I could not find any video footage except for brief mentions. However there were lots of cameras there during the report. How to find the full video?
Valery Legasov's report to the IAEA
Footage of Legasov's address does exist -- but perhaps not the whole address. The relevant passages in Higginbotham's 'Midnight in Chernobyl' with respect to the Vienna Conference say:
Two weeks later, on August 25, Valery Legasov, wearing a gray suit and striped tie, his face puffy and haggard behind thick glasses, took the floor on the opening day of the special technical conference at IAEA headquarter in Vienna. 
: Two weeks later, on August 25: Walter C. Patterson, “Chernobyl-The Official Story,” Bulletin of the Atomic Scientists 42, no. 9 (November 1986): 34-36. For archival footage of Legasov's IAEA appearance, see the documentary film The Mystery of Academician Legasov's Death [Тайна смерти академика Легасова], directed by Yuliya Shamal and Sergei Marmeladov (Moscow: Afis-TV for Channel Rossiya, 2004).
The documentary, The Mystery of Academician Legasov's Death [Тайна смерти академика Легасова], is accessible on YouTube. 29:15 takes you to Vienna, but it is (obviously) not the entire five-hour delivery Legasov gave (nor the "several hours of questions") Higginbotham refers to.
A potential negative statement for a better version of the footage existing is that if it did, then Higginbotham should have referred to that in lieu of the Shamal & Marmeladov documentary. Alternatively, if such a footage existed, it might be under distribution restrictions.
I would perhaps leave you with the USSR's 'The Accident at the Chernobyl Nuclear Power Plant and Its Consequences: Information compiled for the IAEA Experts' Meeting, 25-29 August 1986, Vienna' which is the closest I saw to what Legasov would have been talking about (given you wanted to compare this information with the Legasov tapes).
I asked IAEA Archives (using their contact form) about whether they had this footage, and this is the reply:
While the IAEA does not have an audio or video recording of the Post-Accident Review Meeting, please see the report from the USSR State Committee on the Utilization of Atomic Energy, “The Accident at the Chernobyl Nuclear Power Plant and Its Consequences,” delivered to the Post-Accident Review Meeting in August 1986, which Mr. Legasov attended. That can be found here: https://inis.iaea.org/collection/NCLCollectionStore/_Public/18/001/18001971.pdf?r=1&r=1
If you are looking for other writings from Mr. Legasov, I would suggest that you take a look at INIS: https://inis.iaea.org/search/search.aspx?orig_q=legasov
Mr Legasov also contributed an article to this issue of the IAEA Bulletin in 1987, which focused on nuclear safety: https://www.iaea.org/publications/magazines/bulletin/29-4
There are also additional resources available in the IAEA library catalogue, such as the "Summary report on the post-accident review meeting on the Chernobyl accident : report by the International Nuclear Safety Advisory Group (INSAG - IAEA Safety Advisory Group 7), Vienna 1986 (Safety Series 75-INSAG-1, STI/PUB/740). You can contact the IAEA library Contact here: https://www.iaea.org/resources/library/visitor-information
If the IAEA Archives don't have this, I'm guessing the full conference might not have a surviving record.List of site sources >>>