When Tyrant of Discord enters the battlefield, target opponent chooses a permanent they control at random and sacrifices it. If a nonland permanent is sacrificed this way, repeat this process.
5/1/2012 Repeating the process includes the instruction to repeat the process. That is, the opponent will keep sacrificing permanents until they sacrifice a land.
5/1/2012 Repeating the process does not include targeting an opponent. Only one opponent will have to sacrifice permanents.
5/1/2012 If any abilities trigger while Tyrant of Discord’s enters-the-battlefield ability is resolving, those abilities will wait until the enters-the-battlefield ability finishes resolving before going on the stack. Starting with the active player, each player puts their abilities on the stack in any order.
5/1/2012 If the target opponent can’t sacrifice permanents (perhaps because of Sigarda, Host of Herons), the opponent will choose a permanent at random but not sacrifice it. The ability will then finish resolving.