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