First, to get the ancient totems of demolition to spawn (yes, there are two of them that spawn), you need to survive approximately from forty seconds to one minute IN ANY ROUND without killing any of the enemies. So you can make them spawn even in round one if you really want (a really bad idea).


A good idea for a fast (and risky) way to get the achievement on low rounds is to first stockpile nukes from the black market a couple of times and then try to destroy the totems (for example in round 3).


Note that to make the obelisks spawn, you must NOT destroy enemy ships for approximately forty seconds. The bombs dropped from enemies do not seem to count, so you should try to defend your shields from these bombs while trying to get the obelisks to spawn.

A good idea is to destroy enemies until the last enemies of the round spawn and let them hover in formation over the city while defending against the bombs the enemies drop:


The obelisks are crazy enemies, as they launch the bigger nukes that approach your city at crazy speed. Thus, having a big stockpile of your own nukes (preferably the normal nukes or antimatter nukes, as the smaller nukes have a smaller impact area) is crucial to do damage against the obelisks and make their nukes explode before they annihilate your city.

Beware of the enemy nukes!