I have googled this extensively and only see results for the demand(s) that Serbia did not meet causing the war to start, but no where do I see a list of the others. Thanks for your time!
(I am writing this on my phone, so hopefully the formatting won't be too bad or confusing, I will also be translating and paraphrasing the text rather than providing the entire quote, I do not have any English version at hand at the moment)
The ultimatum sent by the Austro-Hungarian Monarchy consisted of 10 points as well as a demand for public apology.
The first demand was the public apology (the text itself being prepared by the Austro-Hungarian goverment) which was to be issued by the Serbian goverment to both the public as well as the army. To paraphrase the text itself, it basically says that the Serbian government regrets what happened as well as it regrets the participation of Serbian army officers and state officials in the assassination, that it ran contrary to the declaration of the Serbian government in 1909 and that it promises it will prosecute those involved in the deed harshly.
Now to the meat of the ultimatum which are the infamous 10 points:
The Royal Serbian Government is obligated to:
surpress any publication that incites hatred against the Monarchy and which aims towards compromising its territorial integrity.
immediately dissolve 'Narodna Odbrana' as well as any other organization or association that spreads propaganda against Austria-Hungary and make necessary precautions for those organizations and associations to not continue their activity under different name or in different form.
immediately remove personnel and teaching material from public schools that serve or could serve as propaganda against Austria-Hungary.
remove all officers and state officials from the army and the administrative who are guilty of spreading propaganda against Austria-Hungary with the Imperial and Royal goverment reserving the right to convey their names to the Royal Serbian government and disclose proofs.
allow the organs of the Imperial and Royal government to cooperate in Serbia with suppression of subversive movements aimed against the territorial integrity of the Monarchy.
conduct investigation against all the participants of the conspiracy from 28th June who are currently in Serbia, and allow the organs of the Imperial and Royal government to participate in the investigation.
immediately arrest major V. Tankosić and certain M. Ciganović, Serbian state officials who were compromised by the results of the investigation.
implement effective measures to prevent parts of the Serbian administrative from smuggling and transporting ammunition across the border and dismiss and harshly punish the border officers in Šabac and Loznica who assisted the criminals of Sarajevo with crossing the border.
give the Imperial and Royal government an explanation regarding the inexcusable statements made by prominent Serbian officials in Serbia and elsewhere who, with no regard to their official standing, decided to give hostile public statements against Austria-Hungary after the assassination.
immediately inform the Imperial and Royal government that all measures included in the previous points were implemented.
source: VESELÝ, Zdeněk et al. Světová politika 20. stol. v dokumentech (1900-1945), 2000