Play a lightning round scenario on the chieftain difficulty and pick the civilization you need to complete.
One condition to win the lightning round is to research Atomic Theory first.
Follow these simple rules:
1. Set all cities to produce science
2. Build the library (2x science), the Courthouse and the university (4x science) as they become available, after that build aqueducts if needed after that
3. Change you government to Democracy as soon as you learn it
4. When you meet a new civilization, be peaceful "Yes, Let us have peace"
5. Always answer "Your threats do not frighten us" or "We have not need of" (don't give the other civilizations anything)
6. Don't explore the map
7. Put all units into defensive mode (the shield)
8. Utilize any great person immediately, however it is best to have them complete whole research items that are over 4 to 5 turns
9. Have any settlers that appear join your city
10. Don't wory bout any attackers. Your starting units and the few that you will gain from research are more than enough. You may loose a city, but it is usually during the last stretch of research (Electricity or Atomic Theory) that it doesn't matter
Recommended order of research:
Alphabet
Writing
Literacy
Code of Laws
Democracy (change government when completed)
Mathematics
Engineering
Univerisity
Invention
Steam Power
Metallurgy
Electricity
Atomic Theory
This strategy works for all of the following achievements: