Here is the full list of all 64 Hexarchy achievements.
Lose a multiplayer game
Place top 3 in a ranked multiplayer game
Complete a Daily Challenge
Get 1st place in a game with all 10 civilizations
Win a game with only one city
Win a game without building any Wonders
Win a game using only Ancient technology
Win a game without researching any technology
Research all 24 Techs in a single game
Grow a city to 10 population
Control 5 cities
Control 100 hexes
Pillage an enemy city
Burn the Great Library card
Control 50 hexes
Have a unit survive 5 battles
Complete the Starter Campaign
Capture an enemy city
Grow a city to 5 population
Grow a city to 20 population
Grow a city to 30 population
Pillage 5 enemy cities in a single game
Control 10 cities
Control 15 cities
Complete 3 straight Daily Challenges
Complete 10 straight Daily Challenges
Complete a Weekly Campaign
Complete 4 straight Weekly Campaigns
Be first place on the Daily Challenge leaderboard
Be first place on the Weekly Campaign leaderboard
Control all 13 Wonders in a single game
Win a game without attacking with your units
Win a game without fighting with your units
Kill a unit from every player on a large map
Eliminate every player on a large map
Capture 100 enemy cities
Pillage 50 enemy cities
Construct 200 Wonders
Research 400 Technologies
Adopt 200 Civics
Claim 500 enemy hexes with culture
Win a ranked multiplayer game
Complete 10 ranked multiplayer game
Place top 3 in 10 ranked multiplayer games
Place top 3 in 20 ranked multiplayer games
Kill 25 enemy units in a ranked multiplayer game
Place first in 20 multiplayer ranked games
Deal 50 damage in a single hit
Deal 100 damage in a single hit
Have a unit survive 10 battles
Finish first place on a Daily Challenge leaderboard
Finish top 5 on a Daily Challenge leaderboard
Finish first place on a Weekly Campaign leaderboard
Win a weekly hegemon round at the Squire contribution level
Win a weekly hegemon round at the Knight contribution level
Win a weekly hegemon round at the Hero contribution level
Win a weekly hegemon round at the Legend contribution level
Win 5 weekly hegemon rounds
Complete a weekly hegemon round at the Legend contribution level
Resume a Game
Resume 5 Games
Build a boat
Build a city on another continent
Pillage 5 Wonders and burn 5 Wonder cards in a game