READ THIS FIRST

Achievements are bugged in newest version of the game. You need to downgrade your game version to 1.09, disable internet connection and make few adjustments to make everything to work. I won't tell you how to do everything about downgrading your game. There is a wonderful guide made by another player that will help you how to downgrade and fix this game properly.

GUIDE OF DOWNGRADING A GAME TO 1.09 FOR ACHIEVEMENTS!
https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=3489276236
After setup, you can start your MAFIA III journey.

There is a bug that can corrupt you save file! To prepare for this, there's a guide showing how you can fix this problem by simply restoring your save after a crash. This mission is really unpredictable and I want you to be fully prepared when playing this DLC.

GUIDE TO PREVENT SAVE FILE CORRUPTION!
https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=3499814361

Story trophies can't be missed

• Somethin' I've Gotta Do
  
• Standard Communication Grid
  
• Pray on the Way Up
  
• For Old Time's Sake
  
• Fish Gotta Eat
  
• We Partners Now
  
• It's a Brave New World
  
• Cut & Run
  
• Sure Thing, Boss
  
• Everyone Will Notice
  
• Little Late for That
  
• The Poor Sumb****
  
• The Connection to Cuba
  
• My Name is Lincoln Clay
  
• Burn Like Napalm
  
• Certainly Was Exciting
  
• Real Nice Time
  
• Jesuit in New Mexico
  
• There's a War Goin' On
  
• Yet Here We Are
  
• Before They Bury You

There is nothing to say about these trophies because you will unlock them eventually. Non of these are or should be bugged so don't worry.

After setting up the game, you should be able to achieve everything related to the achievements. Before starting, you will need to play this game 2 times for business rackets related reasons. Decide which route you will take for the 1st and 2nd playthrough.
Killing everyone

• Can't Trust a Rat
  Killed 15 Racket Informants
  
• No Loose Ends
  Killed all of the Racket Bosses

Recruiting everyone

• Live Another Day
  Recruited 15 Racket Informants
  
• The New Boss
  Flipped 16 Racket Bosses

Flipping a racket will require you to wiretap region where racket hideout is set in for ability to recruit option to appear in the first place.
These achievement are bugged in the newest version of the game but with 1.09 guide – everything should work perfectly.

UNDERBOSS
This was first playthrough I took and ran with it grabbing easier trophies related to the game and giving all the districts to one Underboss, for me it was VITO . If you go with one underboss the whole game you will unlock:

• Just You and Me
  Kept only one Underboss alive until "Yet Here We Are"
  
• Trust
  Reached the Loyal state with one Underboss
  
• Big Earner
  Received $10,000 in earn from one Underboss

To receive $10,000 from a underboss you need to complete optional missions for him and his lieutenant. When you see "Kickback" is $10,000 on the map, go and collect it by yourself.

DRIVING

• Custom 358
  Drove at 120 mph or faster for 20 seconds
  Take a exotic car a head down to highway. Easier done in late-game because you receive upgrades for all your cars (acceleration + speed).
  
  
• New Bordeaux Drifter
  While driving, drifted for at least 5 seconds
  Shooting your tires helps.
  
  
• One Good Turn
  Made a 180 degree turn at high speed without hitting anything.
  
  
• Wrecker
  Executed 10 Vehicle Takedowns
  Works also on police vehicles.

KILLING

• Flambé (Fixed in 1.09)
  Made 10 enemies kill themselves with their own Molotovs
  Start doing this as early as possible because late game enemies start using hand grenades. When enemy is about to throw molotov on you, they will shout out loud so always try to hear their communication.
  
  
• Combat Specialist (Fixed in 1.09)
  Killed 300 enemies using Takedowns
  
  
• Shh, shh (Fixed in 1.09)
  Performed 100 Stealth Takedowns on enemies
  
  
• Closed Casket (Fixed in 1.09)
  Performed 50 Brutal Takedowns
  
  
• Sending A Message
  Chained together 3 or more Brutal Takedowns
  
  
• Pop, Pop (Fixed in 1.09)
  Killed 4 enemies using Slow-Mo Shooting 10 Times
  Before Prostitute racket, you will unlock this ability. Start using as often as possible and shoot as many headshots as possible. To enter Slow-Mo press SPACE after aiming.
  
  
• Softened 'Em Up
  Completely weakened a Racket by killing all of its Enforcers
  
  
• I'm Goin' In!
  Attacked a Racket without killing any Enforcers

These achievements were bugged but in version 1.09 fixes them and you will get them eventually by making takedowns. Just remember to make takedowns with Q button as often as possible.


MONEY

• Cash in Hand
  Saved $150,000 between your wallet and the bank
  
  
• Baby, You're a Rich Man (Fixed in 1.09)
  Earned $500,000
  Don't spend money if you're going after this one. You will need to save everything you have up until the end game. Try to explore every possible enemy racket or objectives given by informants.
  
  
• Hole in Your Pocket (Fixed in 1.09)
  Spent at least $500,000
  After earning $500,000, there is a lot of things you can spend your hard earn cash. Simply start buying special weapons and upgrades.

UNDERBOSSES
In the second run, I did everything I did in the first one, the only difference was I recruited every racket boss and informant and kept every underboss alive for achievements:

• We're in This Together (Fixed in 1.09)
  Kept all Underbosses alive until "Yet Here We Are"
  To keep everyone until the end and happy, you need to give every underboss 3 districts. Always try to go for a ABC rotation. For example – 1st district CASSANDRA, 2nd BURKE, 3rd VITO (ABC rotation). After that, go again with ABC. Do it for 3 cycles so everyone gets 3 districts each.
  
  
• Family (Fixed in 1.09)
  Reach maximum loyalty rank with each of the underbosses
  After giving away 3 districts each. You can start ending their side-quests. To get max loyalty, complete boss and lieutenant side quests and you should receive the achievement.
  
  
• IRA Don't Ask
  Completed all of Burke's side-missions
  
• I Need a Favor
  Completed all of Vito's side-missions
  
• .45 in My Hand
  Completed all of Cassandra's side-missions

These are the most important achievements from this DLC.

• Campaign Strategy
  Destroyed 10 of Slim's re-election billboards
  You will see lot of these, it's easy to spot. You will get this over time.
  
  
• Danger Close (Fixed in 1.09)
  Killed 30 enemies using Proximity Mines
  Always stack as much as possible. When you have chance, always try to hit a group of enemies. Throw these straight into an enemy, not in the position they are moving. Start doing as soon as possible. Also, police units count as enemies.
  
  
• Trap Game Strong (BUGGED)
  Successfully triggered 10 Vehicle Traps
  You will need to complete this in one sitting. It isn't that hard. There is a road on north side that has 4 of these and they re-spawn quickly.

These are the most important achievements in this DLC.

• Operation: Deep Sleep
  Knocked out 30 people with the Dart Gun
  You will get this weapon after finishing the DLC, introduction of bounty hunting. Civilians count for this achievement.
  
  
• Big Fat Party Animal
  Killed 50 enemies using the Hartmann 7.62mm and wearing the Party Animal outfit
  Killing police officers count as enemies.
  
  
• Spotter (BUGGED/FIXED?)
  Killed 30 Enemies Using Sniper Support
  You have to do this in one sitting. Update: @Ikona mentions, that during missions, you can load last checkpoints during shootouts so you can farm kills like this, which saves a lot of time. Always take Sniper Support kit from the marshals hideout, don't buy them, too expensive... You can drive to the nearest bridge and it spawns in the same place. Civilians don't count as kills, you need to kill enemies or police officers. This achievement is the most annoying achievements done in Mafia III, for me at least.

AS I MENTIONED IN THE BEGINNING OF THIS GUIDE – LOOK UP FOR THE GUIDE I LEFT TO PREVENT SAVE FILE CORRUPTION!

These are the most important achievements of this DLC.

• Blade of Death
  Killed 20 enemies using Throwing Knives
  You will unlock these mid way of the DLC. Start killing everyone and you will get this easily.
  
  
• Street Rocket
  Drove a distance of 50 km in the Samson Harrier
  To get this car, you will need to start renovating Sammy's. Upgrade Sammy's and repair the bar. After couple of upgrades, side-quest should appear that will unlock this vehicle then completed. It will take around 15-20min driving around the city to get this achievement.

This game has great story elements but it's torture to enjoy completing this game fully. To think that you need to downgrade to older version of the game and even disconnect it from the internet is crazy work. At least you can get the Platinum now!

Drop your suggestion or other important notes down in the comments!