Be warned, there could be some potential story spoilers in this article.
Xbox Achievements has managed to get their hands on the entire achievements list for Fallout 4 ahead of it's launch on November 10. Whilst the list only applies to the Xbox One achievements, the PlayStation 4 Trophies are expected to be very similar.
Below, the achievements have been listed. Interestingly, there are only level achievements up to level 50, despite there being no level cap.
+ War Never Changes - Enter The Wasteland
+ When Freedom Calls - Complete "When Freedom Calls"
+ Unlikely Valentine - Complete "Unlikely Valentine"
+ Reunions - Complete "Reunions"
+ Dangerous Minds - Complete "Dangerous Minds"
+ Hunter/Hunted - Complete "Hunter/Hunted"
+ The Molecular Level - Complete "The Molecular Level"
+ The Nuclear Option - Complete "The Nuclear Option"
+ Institutionalized - Complete "Institutionalized"
+ Mankind-Redefined - Complete "Mankind-Redefined"
+ Powering Up - Complete "Powering Up"
+ Nuclear Family - Complete "Nuclear Family"
+ The First Step - Join the Minutemen
+ Taking Independence - Complete "Taking Independence"
+ Old Guns - Complete "Old Guns"
+ Semper Invicta - Join the Brotherhood of Steel
+ Blind Betrayal - Complete "Blind Betrayal"
+ Ad Victoriam - Complete "Ad Victoriam"
+ Tradecraft - Join the Railroad
+ Underground Undercover - Complete "Underground Undercover"
+ Rockets' Red Glare - Complete "Rockets' Red Glare"
+ Sanctuary - Complete "Sanctuary"
+ Community Organizer - Ally with 3 Settlements
+ Benevolent Leader - Reach Maximum Happiness in a Large Settlement
+ Gun-F-Hire - Complete 10 Side Quests
+ Mercenary - Complete 50 Misc. Objectives
+ Scavver - Gather 1000 Resources Used For Crafting
+ What's Yours Is Mine - Pick 50 Locks
+ RobCo's Worst Nightmare - Hack 50 Terminals
+ Armed and Dangerous - Create 50 Weapon Mods
+ Wasteland D.I.Y. - Craft 100 Items
+ Never Go It Alone - Recruit 5 Separate Companions
+ Lovable - Reach Maximum Relationship Level with a Companion
+ Fix-Er-Upper - Build 100 Workshop Items
+ Future Retro - Play a Holotape Game
+ ...The Harder They Fall - Kill 5 Giant Creatures
+ Ranger Corps - Discover 100 Locations
+ Print's Not Dead - Read 20 Magazines
+ Prankster's Return - Placed A Grenade Or Mine While Pickpocketing
+ Masshole - Kill 300 People
+ Animal Control - Kill 300 Creatures
+ Homerun! - Get a Homerun
+ Touchdown! - Get a Touchdown
+ They're Not Dolls... - Collect 10 Vault-Tec Bobbleheads
+ ...They're Action Figures - Collect 20 Vault-Tec Bobbleheads
+ Born Survivor - Reach Level 5
+ Commonwealth Citizen - Reach Level 10
+ Unstoppable Wanderer - Reach Level 25
+ Legend of The Wastes - Reach Level 50
+ Prepared for the Future - Decide the Fate of the Commonwealth