Finish at least one wave on each map in Infestation.

There are 16 maps in total. The first 8 are unlocked immediately and are called the following:

Black Market
Trapped
Heretic
Extermination
Meltdown
Pressure
Dust to Dust
Harvest

The other 8 which are locked are simply 'DARK' versions of the maps above. To unlock each DARK version you have to complete 5 waves on the regular version. For example, if you complete 5 waves of Black Market you will unlock Black Market 'Dark'.
Therefore you will there be required to complete at least 48 waves (40 regular + 8 DARK) across all the maps for the Achievement to unlock.
They can be done either online with other players or offline solo or a mixture of both. They will all count towards the Achievement.