A list of the achievement names for Max Payne 3 has been made public. The secret ones are not listed below but if you want to remain spoiler free even from the relatively vague names, then don't read the list at all. It's just that simple!
List courtesy of CVG.
Feel the Payne
Story Complete [MEDIUM]
Serious Payne
Story Complete [HARD]
Maximum Payne
Story Complete [OLD SCHOOL]
Payne In The Ass
Story Complete [HARDCORE]
It's Fear That Gives Men Wings
10 Bullet Time Kills In A Row
You Could Hurt Somebody With That
Shoot 10 Airborne Grenades
You Sure Know How To Pick A Place
Discover All Tourist Locations
The Fear Of Losing It
Survive A Level Without Painkillers
One Bullet At A Time
300 Headshots
You Play, You Pay, You Bastard
100 Kills With Melee
With Practiced Bravado
100 Kills During Shootdodge
Past The Point Of No Return
Take 100 Painkillers
A Few Hundred Bullets Back
Use Every Weapon In The Game
Colder Than The Devil's Heart
Kill 30 Enemies In 2 Minutes
Part I Complete
Complete Part I Of The Story
Part II Complete
Complete Part II Of The Story
Part III Complete
Complete Part III Of The Story
Out The Window
Get 6 Kills While Diving Through The VIP Window [FREE AIM]
The One Eyed Man Is King
Cover Passos With Perfect Aim
That Old Familiar Feeling
Clear The Hallway Of Lasers
Something Wicked This Way Comes
Get 7 Kills While Jumping From The Rickety Boat [FREE AIM]
Amidst The Wreckage
Destroy All The Models In The Boardroom
So Much For Being Subtle
Get 9 Kills While Being Pulled By A Chain [FREE AIM]
The Shadows Rushed Me
Unlock And Complete New York Minute Hardcore
The Only Choice Given
Get 8 Kills While Dangling From A Chain [FREE AIM]
Along For The Ride
Trigger A Bullet Cam On The Zipline [FREE AIM]
Sometimes You Get Lucky
Get A Headshot During The Rooftop Tremors
It Was Chaos And Luck
Get 6 Kills While Riding The Push Cart [FREE AIM]
The Road-Kill Behind Me
Total Everything On The Runway
Trouble Had Come To Me
Clear Everyone On The Bus Ride
All Of The Above
Finish All Grinds
An Echo Of The Past
Find All Clues
A License To Kill
Collect All Golden Guns
A New York Minute
Finish In A New York Minute
Full Monty
Complete One Of Each Game Mode Including All Gang Wars
Payne Bringer
Kill 100 Other Players
Max Payne Invitational
You Invited Someone To Play
Man Of Many Weapons
Unlock All Weapons
Man Of Many Faces
Unlock All Faction Characters
Deathmatch Challenge
Winner In Any Deathmatch
Grave Robber
Looted A Body
The Gambler
Won A Wager
Training Complete
Achieve Level Rank 50
Dearest Of All My Friends
Kill Someone On Your Friends List
Story Complete [MEDIUM]
Serious Payne
Story Complete [HARD]
Maximum Payne
Story Complete [OLD SCHOOL]
Payne In The Ass
Story Complete [HARDCORE]
It's Fear That Gives Men Wings
10 Bullet Time Kills In A Row
You Could Hurt Somebody With That
Shoot 10 Airborne Grenades
You Sure Know How To Pick A Place
Discover All Tourist Locations
The Fear Of Losing It
Survive A Level Without Painkillers
One Bullet At A Time
300 Headshots
You Play, You Pay, You Bastard
100 Kills With Melee
With Practiced Bravado
100 Kills During Shootdodge
Past The Point Of No Return
Take 100 Painkillers
A Few Hundred Bullets Back
Use Every Weapon In The Game
Colder Than The Devil's Heart
Kill 30 Enemies In 2 Minutes
Part I Complete
Complete Part I Of The Story
Part II Complete
Complete Part II Of The Story
Part III Complete
Complete Part III Of The Story
Out The Window
Get 6 Kills While Diving Through The VIP Window [FREE AIM]
The One Eyed Man Is King
Cover Passos With Perfect Aim
That Old Familiar Feeling
Clear The Hallway Of Lasers
Something Wicked This Way Comes
Get 7 Kills While Jumping From The Rickety Boat [FREE AIM]
Amidst The Wreckage
Destroy All The Models In The Boardroom
So Much For Being Subtle
Get 9 Kills While Being Pulled By A Chain [FREE AIM]
The Shadows Rushed Me
Unlock And Complete New York Minute Hardcore
The Only Choice Given
Get 8 Kills While Dangling From A Chain [FREE AIM]
Along For The Ride
Trigger A Bullet Cam On The Zipline [FREE AIM]
Sometimes You Get Lucky
Get A Headshot During The Rooftop Tremors
It Was Chaos And Luck
Get 6 Kills While Riding The Push Cart [FREE AIM]
The Road-Kill Behind Me
Total Everything On The Runway
Trouble Had Come To Me
Clear Everyone On The Bus Ride
All Of The Above
Finish All Grinds
An Echo Of The Past
Find All Clues
A License To Kill
Collect All Golden Guns
A New York Minute
Finish In A New York Minute
Full Monty
Complete One Of Each Game Mode Including All Gang Wars
Payne Bringer
Kill 100 Other Players
Max Payne Invitational
You Invited Someone To Play
Man Of Many Weapons
Unlock All Weapons
Man Of Many Faces
Unlock All Faction Characters
Deathmatch Challenge
Winner In Any Deathmatch
Grave Robber
Looted A Body
The Gambler
Won A Wager
Training Complete
Achieve Level Rank 50
Dearest Of All My Friends
Kill Someone On Your Friends List
List courtesy of CVG.