So much so it is not worth it to me to have Civ 5 installed if I have to have Steam installed.As said by Brian Schkerke you cannot legally play Civilization5 without steam.Edit: this was a temporary bug that was fixed in an update about a month or two after this discussion.The above response has not been applicable for years!
There are ways around the installation of Steam but if you're particular about Steam being installed, I doubt you want to investigate the alternate avenues. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).
You will however still need to run the Steam client in the background as Civ5 plays.
This may be un-palatable for your tastes but at least it is a 'neutered' version of Steam which does not connect to the internet or use up your system resources.
Could it be that I cannot unlock the bronze until I complete the silver ones?
What other reason is there for not getting the achievement?