Here is the full list of all 15 Big Bang West achievements.
Finished all of the levels
Completed 50 events
Built 10 Deluxe Houses
Built 10 Houses
Built a city with a least 150 inhabitants
Trained and kept at least 10 sheriffs
Have income at least $1,000/day
Earned 10,000 pieces of dollars
Imprison 10 bandits
Have income at least $500/day
Built a city with a least 80 inhabitants
Finished at least 10 levels with a Gold Trophy
Your town level was at 5 or higher
Finished at least 3 levels with a Gold Trophy
Finish the first level