this achievement is really not that hard, as long as you have patience, a little bid of combat skill and as long as you remember everything you've done
so first of all you want to do the following:
*beat all story missions (94) these ones require some skill, but arent impossible. you know you are done with this as soon as you get the "You won!" achievement
*once you are done with this you want to complete all 10 of Little Jacob's courier package jobs. you can start these after the mission Shadow, early in the game. you are done with this as soon as you get the "Courier service" achievement
*then you want to start to check your emails from brucie, which you can do after the mission Logging on. he will send you some emails about 10 vehicles he wants to be stolen. if you send him a possitive reaction you will begin the mission. you are done with this as soon as you unlock the "Order Fullfilled" achievement
*now you should start to check your text messages from Stevie. he'll send you the locations of 30 vehicles he wants to be stolen. check out youtube for the locations. when you steel one of the vehicles the game will tell you and you want to go to your garage in Bohan and park your vehicle in here. you dont have to worry about this once you have the "You Got the Message" achievement
*now we want to look for some police cars. steel one and access the computer. you should go to current crimes and choose one. now you start a mission in which you must kill some criminals. complete 20 crimes and youre done with this and you obtain the "Cleaned the Mean Streets" achievement
*now we keep our police car and we're going to look for the most wanted. there will be 10 criminals you want to visite and to shut up. once you are done with the first 10, you should go to the other islands (alderny (west), algonquin (middle) and Bohan/Dukes/Broker (East)) and complete the remaining 20 most wanted missions and you should get the "Manhunt" achievement
*now we should go to alderny (the left island) and, after you have completed the mission Truck Hustle, there should be an Assassination mission on your map. you will need to complete all 9 missions and you will obtain the "Assassin's Creed" achievement
*now you should call brucie to do some races. you need to complete at least 9 of them. but you may want to do 11 more so you get the "Genetically Superior" achievement (THIS IS NOT NEEDED FOR THE KEY TO THE CITY ACHIEVEMENT, but if youre going for achievements, why not grab this one on your way)
*the next thing to do is doing all the random character missions. you can find the locations of these on youtube (YOU DO NOT NEED TO COMPLETE THE MISSIONS FROM IVAN, CHERISE, CLARENCE AND JEFF) you have met all 10 strangers at least once once you get the "No more Strangers" achievement (BUT YOU'LL NEED TO COMPLETE EVERY MISSION OF THEM)
*now you can start to hang out with your friends Brucie, Little Jacob and Packie. call them and complete every activity with these 3 friends at least once (thats about 30 activities) there is no Achievement for this, but you will obtain the "Dial B for bomb", "That's How We Roll!" and "Retail Therapy" achievements when you unlock their special abilities (THIS IS ALSO NEEDED FOR 100%) you may as well hang out with your two other friends (if they are still alive) and grab the "Liberty City (5)" achievement (not needed for 100%)
*now we're going to play some games and we must win a FULL game of bowling with a friend, a game of darts and a game of pool which gives you the "Pool Shark" achievement
*now you should look for a QUB3D machine (there is one at the strip club in Bohan) and play this mini game. when you beat the high score (11000) you get the "King of QUB3D" achievement
if you did everything correctly so far, you should have 95%, two more things to do
*one of the harder things to do is to complete all stunt jumps. find a list of them on youtube and start completing all 50 of them and you'll get the "Dare Devil" achievement
*now the hardest and most boring thing to do: find and eliminate all 200 pigeons. i would really recommend to use the list on youtube from Roosterteeth. killing these pigeons is time wasting and boring and will often get you the cops after your ass, but will give you the "Endangered Species" achievement
and then finally you will get the "Key to the City" achievement
i hope this guide helps :D