This can be completed in casual or classic mode and just requires one play and completion of each of the available levels, no medals need to be earned and overall rank doesn't matter either.
* is a semi-boss level that requires 3 DNA antibodys, if the Antibody is grey you'll need to play a level with that enemy type in to earn one.
** is just a boss fight, costing 1-3000 credits depending on the stage and 3 DNA antibodys.
Coral Lake East: 5
A Recruit's Duty
Broken Bonds
The Draco Connection
A plague of Vespin *
The Bloated Anomaly **
Coral Lake West: 4
Pest Control
New Blood
Lockdown
Holding the Line
Underground Lake: 4
The Subterranean Outbreak
An Experiment
Stemming the Tide
The Monster Underground *
One thing to note is there is no tracking bar for completed missions for this achievement and it can glitch and not pop, I actually earned this one a day earlier than it says due to this. If it doesn't pop when you finish the final mission of the group, reboot the XOne and that should clear it. If not and it doesn't sort itself out then the only way I've seen is to delete the save and redo the missions, this has fixed it everytime but I would recommend leaving it until everything else is completed.