Can't get the Key To The City achievement (100% completion) in GTA IV

I'm trying to get 100% on GTA IV to get the Keys To The City achievement but I'm stuck at 95%.

http://wikicheats.gametrailers.com/Grand_Theft_Auto_IV_-_PS3_XB360/Achievements

I saw that some people are stuck at 99.5% and they said this half percentage point is a random encounter.

What do you think is missing on my game? I already had done everything on the checklist...

Without knowing what you've completed to this point, there's no way to say what you're missing, so all I can suggest is that you go back through and confirm that you have completed everything on the list. I recommend using a more detailed list, like the one here, so that you can ensure you have crossed off every detail for every item. At 95%, you're clearly missing a significant portion of at least one item on the overall list.

If you've got the following achievements, then you'll get the listed percentage toward completion. Make sure you have the achievements and that you are playing from a save on which you got them.

• Story Missions: 60%
  According to the linked post, there are 87 of these. If you got the You Won! achievement with this saved game, then you should have this part done.
• No More Strangers: 5%, but you must also complete the missions the strangers give you
• Cleaned The Mean Streets: 2.5%
• Endangered Species: 2.5%
• Manhunt: 2.5%
• Dare Devil: 2.5%
• Courier Service: 2%
• Order Fulfilled: 2%
• Genetically Superior: 2%
  You need to complete only the first nine races to get the 2% toward completion; the others count only toward the Genetically Superior achievement
• Assassin's Greed: 2%
• You Got The Message: 2%

That leaves 15%. 10% comes from friends (note that percentages for these are not broken out):

Open all unique abilities
You must unlock all unique abilities from friends.
- Brucie - Helicopter
- Little Jacob - Guns
- Packie - Bomb
You do not need to keep the abilities unlocked, you just have to unlock them all at least once.

Complete every possible activity with each friend (Brucie, Little Jacob and Packie)
- You must actually BEAT your friends at pool, darts, and bowling.
- Dwayne, Michelle, and Roman do NOT count towards the percentage.

and 5% comes from games. Note that if you have completed the 10% Friends above, you will also have completed some of the games below:

Beat all games at least once
- Darts vs friend or computer - 1.25%
- Bowling vs friend in a FULL game - 1.25%
- Pool vs friend or computer win - 1.25%
- QUB3D beat high score - 1.25% (also the King of QUB3D achievement)