Here is the full list of all 64 Hexarchy achievements.
Control 5 cities
Have a unit survive 5 battles
Resume 5 Games
Control 50 hexes
Complete the Starter Campaign
Grow a city to 10 population
Resume a Game
Pillage 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
Capture an enemy city
Control 10 cities
Control 15 cities
Control 100 hexes
Complete a Daily Challenge
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
Win a game without building any Wonders
Control all 13 Wonders in a single game
Research all 24 Techs 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
Win a game with only one city
Capture 100 enemy cities
Pillage 50 enemy cities
Construct 200 Wonders
Research 400 Technologies
Adopt 200 Civics
Claim 500 enemy hexes with culture
Get 1st place in a game with all 10 civilizations
Lose a multiplayer game
Place top 3 in a ranked multiplayer game
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
Win a game using only Ancient technology
Win a game without researching any technology
Burn the Great Library card
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
Build a boat
Build a city on another continent
Pillage 5 Wonders and burn 5 Wonder cards in a game