With all the bonuses that Realm of the Mad God offers, in what order should I gain each achievement? What is the most efficient way to gain the most fame in a lifetime?
Well, for one, keep in mind you have to die to collect any fame that's been earned. But, if you're looking to just pad your reputation then I suppose you wouldn't have asked anyway.
This page tells you exactly how your fame is calculated. I won't transcribe it, but pertaining to your question, it kind of matters how you plan on playing your current life.
If you're looking to make this character last as long as possible, I would try to touch on them all, i.e. Slayer of the Gods, Cartographer, Leader of Men, Well Equipped, etc.
If you're looking for a quick blast of Fame, then get your character to a decent level and go for the high fame percentages, i.e. Oryx Killer, Boots on the Ground, etc.
Also, keep in mind that once you hit level 20, you receive fame for every kill you make, albeit quite a lot smaller than XP dealt when under 20.
Hope that helps...fame is a tricky beast and from what I've been hearing on the forums/Reddit threads...it is due for an upcoming revamp, so take what you will from this answer.
When you want to get fame just go out to the center aka "God Lands" and kill anything that moves, but I would reccomend lvl 16 for lower Gods and 20 for the all out GODS.