Mass soldiers works well, red+white soldiers together own. Did challenges 1-7, could do 8, but black was way more efficient.
Just get a pile of contaminations in your deck, put the plague thing, then put all black creatures in. Then add 5 disintegrates for the bureaucrats.
To beat the last mission, put a heavy defense on the area directly above. There are too many turrets to break through. Expand to the left then up as fast as you can. Use battlecruisers to outrange the turrets, as well as support your troops. Once the enemy runs out of most units, you should be still pushing into the middle left island, and defending attacks from the middle right island. You should have taken out their navy. Use your battlecruisers to destroy the turrets on the middle left island. Then push through however you like and win.
For level 11, don't play defensively. The AI sends units to take out your cell, take one back, and take the big cells when he makes them run low. Take advantage of grouping.