This is the first story achievement but it still takes 2 hours until you get it. Maybe faster if you skip all the cutscenes.
Here is an overview of the story missions and when each story related achievement pops. The order is not linear.
Why Take the Chance?
during this mission you can get the following 2 achievements easily:
This Changes Everything
A Taste of the Action
Go Down on Their Own
Never Going to be Over
...Time to Make a Change
Still Pull This Off
Damn if This Ain't a Gas
...A Friend in Jesus
Something I've Got to Do
That's the plan, padre
Old Times Sake
Prostitution
during Prostitution you can get this missable achievement
Smack
1/15 Racket Informants (kill or recruit all 15)
2/15 Racket Informants
during Smack you can get this missable achievement:
1/16 Racket Bosses (kill or flip[recruit] all 16)Kill Ritchie Doucet
That Goes Both Ways
Friends Like These
We Partners Now?
A Nation Once Again
After A Nation One Again I had to do some smaller side missions to get 3 additional Underbosses: Vito, Thomas, Emmanuel.
And in this process I had another 2 Racket Bosses.
2/16 Racket Bosses (Roy Thibideaux)
3/16 Racket Bosses (Andy Turetto)
Cut and Run
Only Way's Forward
Union Extortion
Contraband
Get Michael Grecco
Moonshine
4/16 Racket Bosses (Carl Bevers)
3/15 Racket InformantsProtection
5/16 Racket Bosses (Sonny Blu)
4/15 Racket InformantsKill the Butcher
An Emotional Attachment
After this mission the game fully opens up: You can start all the DLCs (if you own them) and you can start working on these 3 missable achievements:
The Dead Stay Gone
Guns
5/15 Racket Informants
6/16 Racket Bosses (Pete Santini)Garbage
6/15 Racket Informants
7/16 Racket Bosses (Paul "Puppy" Simmons)Get Enzo Conti
Compromised Corruption
Blackmail
7/15 Racket Informants
8/15 Racket Informants
8/16 Racket Bosses (Frankie Bernard) Construction
9/15 Racket Informants
9/16 Racket Bosses (Jimmy Cavar)
Kill Tony Derazio
Sex
10/15 Racket Informants
11/15 Racket Informants
12/15 Racket Informants
10/16 Racket Bosses (“Handsome” Harry Robicheaux)Drugs
13/15 Racket Informants
14/15 Racket Informants
15/15 Racket Informants
11/16 Racket Bosses (Doc Gaston)Kill the Judge
Kill "Uncle" Lou Marcano
PCP
16/15 Racket Informants
12/16 Racket Bosses (Bobby Bastian)Southern Union
17/15 Racket Informants
18/15 Racket Informants
Racket Bosses (Chester Moreau) CAN'T BE RECRUITEDKill Remy Duvall
Kill Olivia Marcano
My Name's Lincoln Clay...
Blood & Oil
Auto Theft
no Racket Informants
13/16 Racket Bosses (Jack “Junior” Holland)Smuggling
no Racket Informants
14/16 Racket Bosses (Walter “Pops” Holland)Kill Frank Pagani: Setup
Kill Frank Pagani: Takedown
Black Market
19/15 Racket Informants
20/15 Racket Informants
15/16 Racket Bosses (Artie Higgins – Recruit)Gambling
20/15 Racket Informants
21/15 Racket Informants
16/16 Racket Bosses (Johnny “Two-Dicks” Peralta – Recruit)
if you recruited or killed all Racket Bosses: one of these 2 achievements should unlock here:
Rescue Alvarez
Kill Tommy Marcano
The last of the 9 districts will be assigned now. If you gave 3 to each underboss you wil get this achievement:
And if you finished their secondary missions (".45 in my hand", "I.R.A don't ask" and "I need a favour") you will get:
Kill Sal Marcano
Before They Bury You