Here is the full list of all 133 New World achievements.
Defeat the boss in the Dynasty Shipyard expedition.
Win your first Invasion.
Defeat the boss in The Depths expedition.
Purchase your first home.
Defeat the boss in the Starstone Barrows expedition.
Reach Stonecutting skill level 200.
Refine 14,000 items on Stonecutter Tables.
Play for 720 hours.
Reach Leatherworking skill level 200.
Reach Weaving skill level 200.
Craft 100 Weaponsmithing items.
Reach Woodworking skill level 200.
Craft 8,000 Cooking items.
Reach Cooking skill level 200.
Complete 100 quests.
Reach Smelting skill level 200.
Personally defeat 500 other players.
Die 50 times (you seem to like doing this).
Win your first Outpost Rush teamplay battle.
Reach character level 60.
Refine 15,000 leather items at the Tannery.
Reach Logging skill level 200.
Refine 14,000 items at Woodshops.
Craft 500 Furnishing items.
Refine 14,000 items with Looms.
Play for 320 hours.
Craft 6,000 Arcana items.
Reach character level 50.
Harvest 50,000 items using a harvesting sickle.
Reach Mining skill level 200.
Fulfill 50 Faction Missions, any type, anywhere.
Collect 175,000 Gathering type items.
Get 32,000 items using a skinning knife.
Reach Harvesting skill level 200.
Reach Tracking & Skinning skill level 200.
Refine 14,000 items in Smelters.
Craft 100 Armoring items.
Craft 4,000 Engineering items.
Dispel 25 Corruption Breaches.
Reach character level 40.
Craft 25 Furnishing items.
Play for 160 hours.
Collect 24,000 wood using a logging axe.
Mine 32,000 items using a mining pick.
Craft 75 Jewelcrafting items.
Join the Syndicate.
Craft 100 Arcana items.
Kill 100 boars.
Reach character level 30.
Play for 80 hours.
Refine 500 leather items at the Tannery.
Refine 300 items in Smelters.
Craft 100 Cooking items.
Kill 100 turkeys.
Kill 100 rabbits.
Search your first supplies container.
Craft 100 Engineering items.
Refine 250 items with Looms.
Refine 500 items at Woodshops.
Repair 25 inventory items.
Reach character level 20.
Refine 500 items on Stonecutter Tables.
Get 1,000 items using a skinning knife.
Collect 1,000 wood using a logging axe.
Mine 1,000 items using a mining pick.
Die for the first time. Well, that surely won't happen again.
Harvest 1,000 items using a harvesting sickle.
Reach character level 10.
Craft 4,000 Armoring items.
Craft 3,000 Jewelcrafting items.
Craft 4,000 Weaponsmithing items.
Revive 200 allies.
Search 10,000 supplies containers.
Reach Arcana skill level 200.
Reach Armoring skill level 200.
Reach Engineering skill level 200.
Reach Furnishing skill level 200.
Reach Jewelcrafting skill level 200.
Reach Weaponsmithing skill level 200.
Reach Fishing skill level 200.
Get all Trade Skills up to 200.
Have a Territory Standing of 300.
Join the Covenant.
Reach a Covenant rank of 5.
Join the Marauders.
Reach a Marauder rank of 5.
Reach a Syndicate rank of 5.
Reach War Hammer Mastery level 20.
Reach Bow Mastery level 20.
Reach Fire Staff Mastery level 20.
Reach Great Axe Mastery level 20.
Reach Hatchet Mastery level 20.
Reach Life Staff Mastery level 20.
Reach Musket Mastery level 20.
Reach Spear Mastery level 20.
Reach Straight Sword Mastery level 20.
Reach Rapier Mastery level 20.
Reach Ice Gauntlet Mastery level 20.
Fulfill 200 Faction Missions, any type, anywhere.
Fulfill 500 Faction Missions, any type, anywhere.
Fulfill 1,000 Faction Missions, any type, anywhere.
Fulfill 4,000 Faction Missions, any type, anywhere.
Complete the fishing quest arc that starts with 'Fishing With Shields'.
Complete 320 quests.
Win your first War.
Win 10 Wars.
Win 50 Wars.
Win 100 Wars.
Personally defeat 5,000 other players.
Personally defeat 10,000 other players.
Win 25 Outpost Rush teamplay battles.
Win 100 Outpost Rush teamplay battles.
Win 200 Outpost Rush teamplay battles.
Kill 100 cows.
Win 10 Invasions.
Dispel 5,000 Corruption Breaches.
Defeat the boss in the Garden Of Genesis expedition.
Defeat the boss in the Lazarus Instrumentality expedition.
Win 50 Invasions.
Win 100 Invasions.
Defeat 10,000 Aeternum enemies while in groups.
Dispel 500 Corruption Breaches.
Own 3 houses you can travel between.