Showdowns are special missions that will draw out a Warchief. Each Warchief has their own, random Showdown that must be completed every time said Warchief needs to encountered.
"Draw out [the Warchief] by killing his Supporters from the shadows."
A number of Uruks will be marked as "Supporters’ and will appear yellow in Wraith Vision. Kill several of these Uruks while undetected to draw out the Warchief. There are many, many more of them than you need to kill, and they respawn pretty quickly. The only way you can really botch this is by dying, but as long as you’re careful and don’t let the alarm be raised on you, this shouldn’t be too difficult.
"Slaughter waves of enemies to force [the Warchief] to face you."
To draw the Warchief out here you’ll need to provoke an Uruk into sounding the alarm. Just pick a fight, and certainly one of the Uruks will run off to do this. After the alarm has been raised your next task is to kill 35 Uruks. Once done, the Warchief (and his retinue) will arrive.
"Challenge [the Warchief] by executing his Supporters in open combat."
Not much subtlety to this Showdown mission-the Warchief has a host of Supporters, and your job is to kill them with Combat or Ground Executions… which is probably the easiest way to kill most Uruks, anyways. Just charge your Hit Streak up and Execute five Supporters and the Warchief will respond.
"Force [the Warchief] to respond by detonating his Grog Stacks."
An easy Showdown mission, all you need to do is destroy three stacks of Grog. You don’t need to remain undetected, but the Grog is usually guarded by a horde of Uruks. A horde of Uruks that will end up very dead if you wisely shoot the Grog Stacks from afar.
"Brutalize [the Warchief’s] favorite, become undetected, and wait for him to arrive."
You have to be undetected to Brutalize a foe, then after Brutalizing the target, you have to become hidden again, so this Showdown is all about stealth.
"Draw out [the Warchief] by turning his Supporters against him."
There will be a number of Supporters you have to Stealth Brand (R2 + Circle) without being detected. Unlike most Showdown missions with Supporters, there are only as many Supporters as you must Brand. Making good use of Attract and Stealth is necessary to accomplish this goal.
"Grab the Supporter and make him squeal for [the Warchief]."
You’ll have to reach an Uruk Supporter and grab them-but not just that, oh no, too simple-you’ll have to hold them for twenty seconds until the Warchief shows up. Obviously this means the Supporter will have to be complete alone, which isn’t going to happen if this mission takes place in a Stronghold with an Alarm active. So, kill any nearby Uruks and don’t let them raise the Alarm.
Strike From Above
Descend on [the Warchief’s] Supporters to draw him out.
Much like the "Assassination" Showdown mission, except that you have to kill Supporters with Strike From Above.
"Force [the Warchief] to respond by unleashing his Beasts."
Free three Caragors without being detected to draw the Warchief out. Pick your targets well, or you may end up having to fight off the beast you just unleashed.