The 15th Anniversary events begin at November 16th 2019, and runs until 10AM at November 30th. This means that you have two full weeks to complete the event.
In order to get this mount, you need to complete a quest that requires you to run three Anniversary-only timewalking raids. Each raid has three bosses, which means that you have to kill a total of nine bosses before this mount is yours. You can do them in any order.
The raids and bosses are some of the most well-known and challenging bosses from The Burning Crusade, Wrath of the Lich King and Cataclysm expansions packs, and the full raid and boss list is as follows;
Chromie's Memory: The Burning Crusade- Kael'Thas Sunstrider
- Lady Vashj
Chromie's Memory: Wrath of the Lich King- Heigan the Unclean
- The Lich King
Chromie's Memory: Cataclysm- Cho'gall
The raids have been confirmed to be in LFR, so you don't have to do them in normal Timewalking difficulty, in contrast to what a lot of people say (here's a source on this claim). Despite this, the bosses are likely to be pretty challenging, since most of these bosses requires a certain amount of coordination to defeat.
However, if you manage to kill all nine bosses, the Obsidian Worldbreak mount will be yours forever. It will be added to your collection, and you can use the mount on any character you would like to. Enjoy your new mount!