This can be done Privately as well but will require a total of 3 players. The person going for this achievement cannot be participating in the fight. They must be watching from the "crowd" in order to vote.
Voting in KoTH in Injustice works differently from Mortal Kombat. Instead of voting after the match with a numbered card, you must vote during Character Selection based of the following choices:
King To Win The Match
King To Win The Match and Challenge
Rival To Win The Match
Rival To Win The Match and Challenge
Using these choices, you can select who you think will win the fight and who will complete the challenge first. The easiest way to get the achievement is to choose option one, "King To Win..." and communicate with your partners so that the King will quickly win the fight. When the fight is over, you will unlock the achievement for voting correctly.
If you are looking for additional boosting partners, pay a visit to the Achievement Trading Thread.