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