Several reports indicate that this trophy does not unlock when you meet the requirements. The only possible solution at this time is to befriend Clyde before he unfriends you at the very beginning BEFORE talking to Cartman.
MISSABLE!
There are a total of 121 friends to make in the game. Some of them are missable! So you need to be careful when you go for this trophy. To make friends in South Park you need to either just talk to them or complete a quest for them; it's mainly the former luckily so it doesn't take too long to get all 120. We have included below a list of all 121 friends, in the order we got them as a friend. We have listed where to get each one and if one of them is missable or not. Please note, it is difficult to track which friends you have and haven't made, your best bet is to just go down this list and compare it to your list by finding the specific friend. If you cannot find one listed here on your friends list, then that's one you are missing.
Complete list of all friends:
Butters - Story-related
Clyde - MISSABLE! - Speak to him before speaking to Cartman.
Scott Malkinson - Kupa Keep - Talk to him
Kenny - Kupa Keep - Talk to him
Mrs. Cartman - Cartman's House - Talk to her
Dougie - Outside Butters' house
Mrs. Stotch - Butters' House - Talk to her
Mr. Stotch - Butters' House - Talk to him
Mom - Your House - Talk to her
Kelly Gardner - Talk to her outside house 1890
Pete - 2nd floor of garage with a toilet in, just next to Kelly
Officer Barbrady - Outside Tom's Rhinoplasty, talk to him
Millie - Behind Unplanned Parenthood, talk to her
Al Gore - Hiding behind a tree next to Tweeks Coffee, talk to him
Damien - Cinema - Sitting near the back, talk to him
Skeeter - Skeeters Bar - Complete "Rats in the Cellar" quest
Bartender - Skeeters Bar - Complete "Rats in the Cellar" quest
Mr. McCormick - Drunk in a hedge outside Skeeter's Bar
Token - Story-related
Mr Broflovski - Outside Kyle's house, talk to him
Francis - Destroy the snowman outside Kyle's house
Tweek - Story-related
Kelly Rutherford - Bus Stop - Talk to her once you have 20 friends
Craig - Story-related
Randy - Story-related
Mrs. Biggle - MISSABLE! - Sitting on the bench outside the post office, talk to her
Santa - Police Station - On the roof of the police station, talk to him
Romper Stomper - Police Station - Get the jail cell key from upstairs, then let him out of his cell
Timmy - Unlock all fast travel points
Jason - Kyle's House - Shop keeper, speak to him
General Disarray - Butters' Lair (Storage 223) - Talk to him inside
Henrietta - Story-related
Michael - Story-related
Pete - Story-related
Firkle - Story-related
Kyle - Story-related
Bill - MISSABLE! - Attack the people attacking him, 2nd time in the school.
Fosse - MISSABLE! - Attack the people attacking him, 2nd time in the school.
Lemmiwinks - MISSABLE! - Found in the fifth grade classroom opposite.
Cartman - Story-related
Chris Donnely - Kyle's House - Talk to him after doing a certain amount of quests for the elf's
Annie - Story-related
Monica - Story-related
Jessie Rodriguez - Story-related
Lola - Post Office - Talk to her once you have 40 friends
Earl of Winnipeg - Story-related
Bishop of Banff - MISSABLE! - Don't kill him, take the pigs balls instead
Prince of Canada - Story-related
Duke of Vancouver - Story-related
Terrance - Story-related
Phillip - Story-related
Princess of Canada - Story-related
Minster of Montreal - Story-related
Douglas - 2nd floor of building next to unplanned parenthood
Wendy - Story-related
Bebe - Story-related
Red - Talk to her after you complete "Heading North" for the girls
Mr. Mackey - Community Center - Finish his side quest "Wasted Cache"
Mr. Kim - City Wok - Finish his side quest "Mongolian Beef"
Amber - Sewers - Part of the "Dropping the kids off" side quest
Cornwallis - Sewers - Part of the "Dropping the kids off" side quest
Simon - Sewers - Part of the "Dropping the kids off" side quest
Crab Person - Sewers - Found at the very end of the sewers, Nagaskai required
Leroy Mullens - South Park Gazette - On the roof
Mr. Hankey - Complete the "Dropping the kids off" side quest
Mrs. Hankey - Complete the "Dropping the kids off" side quest
Jimbo - Jimbo's Guns - Complete "Big Game Huntin' with Jimbo
Ned - Jimbo's Guns - Complete "Big Game Huntin' with Jimbo
Kevin Stoley - Stoley's House - Complete his side quest "Vulcan Around"
Mr. Tweak - Tweek's Coffee - Buy a Speed Ultra Potion
Mrs. Tweak - Tweek's Coffee - Buy a Speed Ultra Potion
Dad - Your House - Talk to him when you have 50 friends
Bradley - Outside Stan's house, use gnome dust to fit under the hedge and talk to him
Stan - Complete side quest "The She-Ogre for Stan
Beary - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Rabbity - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Skunky - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Beavery - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Mousey - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Squirrely - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Deery - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Woodpeckery - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Porcupiney - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Foxy - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Chickadee-y - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Raccoony - Go Right, Up, Right, Down, Right in the Lost Forest to find the Christmas Critters.
Mrs. Marsh - Tom's Rhinoplasty - Buy something from here
Esther - South Park Gazette - Talk to the girl sitting down
Sergeant Yates - MISSABLE! - Complete the "Nazi Bounty Hunter" quest. You can only get this quest while zombies are in town.
Priest Maxi - Complete side quest "Find Jesus"
Jesus - Complete side quest "Find Jesus"
Mayor McDaniels - Town Hall - Complete her side quest "The Homeless problem"
Mrs. McCormick - Kenny's House - Speak to her in the kitchen
Karen - Kenny's House - Speak to her in the living room
Jimmy - Complete his side quest "Magical Songs"
Mr. Slave - Mr Slave's House - Complete his side quest "Mr. Slaves Package"
Filmore, Flora, Quaid, Jenny, Billy, Sally - are all found from a Hide N Seek quest. Refer to THIS video to find their locations.
Nelly - Talk to her after you complete the "Heading North" main quest for the girls
Heidi - Talk to her after you complete the "Heading North" main quest for the girls
Jessie - Talk to her after you complete the "Heading North" main quest for the girls
Allie Nelson - Talk to her after you complete the "Heading North" main quest for the girls
Mrs. Broflovski - Community Center - Complete "PTA Problems" main quest then talk to her
Mr. Garrison - Community Center - Complete "PTA Problems" main quest then talk to him
Mr. Adler - Community Center - Complete "PTA Problems" main quest then talk to him
Principle Victoria - Community Center - Complete "PTA Problems" main quest then talk to her
DogPoo - Kyle's House - Complete side quest "Restoring the Balance"
Underpants Gnome - Your house - Complete side quest "Phase 1"
Shelly Marsh - Stan's House - Speak to her after you complete "The She-Ogre" side quest
Polly Prissypants - Cartman's House - Speak to her with Cartman in your party
Ike - MISSABLE! - Clyde's Fortress - Fart on the firework which he fails to set off.
Chinpokomon Toy Corporation - MISSABLE! - Collect all 30 chinpokomon, some are missable though.
Mr. Hat - Story related
Big Gay Al - MISSABLE! - Answer the iPhone while inside Mr. Slave
Catatafish - Story Related
Sparrow Prince - Story Related
Frog King - Story Related