The most important thing to remember when dealing with spoiled adults is to avoid arguments and stand your ground. Don't let their whining sway your choices or opinions and make it clear that you won't tolerate certain behaviors.
Spoiled adults are used to getting their way. If they don't, they will let everyone who will listen know their opinion. Any negative criticism will be seen as a personal attack. The spoiled adult will rarely admit fault. Establish boundaries and let them know behaviors you won't tolerate. For example, if the aggressor tends to yell when he or she gets frustrated, walk away and refuse to talk to them until they can have an adult conversation. Be firm but don’t get into an argument; if you do, nothing will be accomplished--it will be a fruitless conversation. You'll be wasting time and generate nothing but frustration.
When you refuse to enable their behavior they may act like victims. Stress the fact that they must take responsibility for their own feelings, but do make an effort to validate their feelings. Validation helps them feel like they've been heard. Still, stand your ground. Remember to establish healthy boundaries. In the long run, they might even thank you for helping them learn something.