Here is the full list of all 45 Ephesus achievements.
Talk to Gregorios
Done with prologue
Build your first house
Die
Drown while swimming
Drink 50 beers
Visit brothel
Find the right place to jump and do the Leap of Faith.
Win your first horse race
Win 50 Horse races
Win your first fight bet
Win 50 fight bets
Win 500 fight bets
Kill your first bandit
Kill 50 bandits
Kill 500 bandits
Complete "Welcome to Ephesus"
Complete "A tour around the Agora"
Kill 5000 bandits
Consume your first food
Find and complete "Treasure Hunt" mission.
Consume 50 foods
Consume 500 foods
Consume 5000 foods
Hunt your first animal
Hunt 50 animals
Hunt 500 animals
Hunt 5000 animals
Collect your first wood
Collect 50 wood
Collect 500 wood
Collect 5000 wood
Collect 5000 Dinars
Collect 50000 Dinars
Collect 500000 Dinars
Collect 1000000 Dinars
Collect your first stone
Collect 50 stones
Collect 500 stones
Collect 5000 stones
Catch your first fish
Catch 50 fishes
Catch 500 fishes
Win 500 Horse races