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