Grand Theft Auto III - The Definitive Edition

*This achievement is missable as certain missions can become unavailable if completed out of order. To avoid this make sure you complete all missions available for Luigi and Joey before carrying out Salvatore Leones missions and also make sure you complete Asuka and Kenji’s available missions before doing any for Donald Love. 

See below the list of everything required for 100%, it is recommended that each time you get to a new island you do all the side quests for that island before doing any missions. 

*Missions marked in red and italicized can be missed and will prevent 100% completion if you do. 

Main missions: 

Introduction 

• Give Me Liberty 

Luigi Goterelli (Must all be completed before “Last Requests” for Salvatore Leone) 

• Luigi's Girls (First Day on the Job (15G) unlocked) 
• Don't Spank Ma Bitch Up 
• Drive Misty For Me 
• Pump Action Pimp 
• The Fuzz Ball - See Got This Figured Out (45G) for a missable achievement 

Joey Leone (Must all be completed before “Last Requests” for Salvatore Leone) 

• Mike Lips Last Lunch, See Without a Scratch (40G), for a missable achievement  
• Farewell 'Chunky' Lee Chong, See Planned Ahead (40G), for a missable achievement  
• Van Heist 
• Cipriani's Chauffeur 
• Dead Skunk in the Trunk 
• The Getaway 

Toni Cipriani  

• Taking Out the Laundry 
• The Pick-Up 
• Salvatore's Called a Meeting 
• Triads and Tribulations, See Mob Boss (45G) for a missable achievement 
• Blow Fish 

Salvatore Leone 

• Chaperone 
• Cutting the Grass 
• Bomb Da Base: Act I 

8-Ball   

• Bomb Da Base: Act II 

Salvatore Leone (2) 

• Last Requests (A Marked Man (25G) unlocked along with second island)

Asuka Kasen  

• Sayonara Salvatore (the Mafia will become extremely hostile to you after this mission it is strongly advised that you have completed all side missions on Portland before completing this) 
• Under Surveillance 
• Paparazzi Purge 
• Payday For Ray 
• Two-Faced Tanner (missable if not completed before you complete the mission Grand Theft Aero for Donald Love) 

Asuka Kasen (2) 

• Bait 
• Espresso-2-Go! 
• SAM 

Kenji Kasen (must all be completed before Waka-Gashira Wipeout! For Donald Love) 

• Kanbu Bust-out  
• Grand Theft Auto  
• Deal Steal 
• Shima 
• Smack Down 

Ray Machowski   

• Silence The Sneak  
• Arms Shortage  
• Evidence Dash  
• Gone Fishing  
• Plaster Blaster  
• Marked Man  

Donald Love  

• Liberator 
• Waka-Gashira Wipeout! 
• A Drop in the Ocean (Offshore Delivery (25G) and third island unlocked) 
• Grand Theft Aero  
• Escort Service  
• Decoy 
• Love's Disappearance  

Catalina  

• Ransom 
• The Exchange (Not So Fast (25G) unlocked) 

Phone Missions:
Marty Chonks  - this phone is marked on the map however it at the Bitch'n 'Dog Food factory across from Joey Leone, it only rings during the day. 

• The Crook  
• The Thieves  
• The Wife 
• Her Lover 

El Burro  

• Turismo (see By a Mile (30G) for a mission specific achievement; this mission can be repeated)  
• I Scream, You Scream 
• Trial By Fire 
• Big 'N' Veiny 

King Courtney  

• Bling-Bling Scramble 
• Uzi Rider 
• Gangcar Round-Up  
• Kingdom Come (A Gift from the King (25G) unlocked; Yardies will also become hostile to you) 

D-Ice  

• Uzi Money 
• Toyminator  
• Rigged to Blow  
• Bullion Run  
• Rumble  

Side missions: 
Off-road/checkpoint missions 

• Patriot Playground 
• Multistorey Mayhem - you have to get a Stallion, there’s normally one in the car park and drive it in front of the entrance (the marker will show) 
• A Ride in the Park  
• Gripped! 

RC car missions (See Man Toyz (30G) for more info) 

• Diablo Destruction 
• Mafia Massacre 
• Calamity 
• Rumpo Rampage 

Vehicle missions 

• Paramedic  - Complete all 12 levels 
• Vigilante - kill 20 criminals on each island (60 in total) 
• Firefighter - Put out 20 fires on each island (60 in total) 
• Taxi – Complete 100 fares 

See Furious First Responder (55G) and Where To? (50G) for more info 
 
Import/Export 

• Bring required vehicles to the Portland Harbour Garage, There is a list of vehicles on the front of the garage so you can keep track of what is still needed, a couple of vehicles can't be brought there until later in the game (Dodo) though most can be found driving around Portland regularly. 
• Bring the required emergency vehicles to the Portland Harbour crane (right behind the Import / Export garage), NB: the FBI car and Barracks OL can’t be collected until you’ve reached Staunton Island, and the Tank until Shoreside Vale 
• Bring the required cars to the garage at Pine Creek in Shoreside Vale 

Again there are loads of guides out there about where to find the vehicles needed. The GTA wiki has a good one here.
  
Unique stunts 
 
See Wheels Up (50G)
 
Rampages 
 
There are a total of 20 rampages spread across the three islands. Each rampage has two spawn locations so if you fail one it will then spawn at its second location. Most are easy enough, just make sure that you go in with full health and armour if you can. It's also recommended to do them early on so enemy gangs are less well armed and less hostile. 

A guide to their locations can be found here

Alternatively, see the video below.