5. Manhunt
So you decided to continue taking out Liberty City's most wanted criminals? Well aren't you the high and mighty hero. Now that you've gotten 20 of the most wanted, you only have 10 more left. Why should you go after them? Well for one, you'd be helping out your brothers in blue - the ones you've already slaughtered throughout the story. As well, the citizens of Liberty City will be delighted to know that the most dangerous criminal helped take out some drug traffickers and carjackers. Most importantly, though, you'll get a nice silver trophy to display next to your other fake trophies. Seriously, you might need another imaginary shelf for all those imaginary trophies.
4. Impossible Trinity
Aside from the Three Leaf Clover mission, Museum Piece is one of the most appreciated mission in the game. Perhaps because it is one of the (if not
the) only missions that bring together the three protagonists of GTA IV and EfLC together. This mission is played through from three perspectives when playing the storylines of all three GTA IV games. Getting through this mission gets you the achievement "Impossible Trinity," which is a reference to the trilemma (and perhaps the three protagonists as they appear in this mission). In a nutshell, Rockstar grants you this achievement just for completing the mission. That's not a bad deal. Off-topic but still related, Museum Piece is perhaps the most diverse mission in the game. An Eastern European immigrant works with a Jewish biker to sell diamonds to the Jewish mafia, but get intercepted by Gay Tony's Dominican bodyguard and half the Italian mafia. A lot of intercultural mingling!