Tip for the Harder+ Achievement:
Be VERY aggressive, especially at the beginning. Don't leave soldiers to defend the first three days, for the whole game send single soldiers your perimeter.
Another huge tip:
Survivors who defend the base turn into soldiers. Try to make sure you always have 1 or 2 survivors defending as they'll become soldiers the next turn.
Early game, the rest of your units should scout aggressively while leaders and new leaders you find recruit, at 2+ leaders go for 25% risk.
Throughout the whole game, do not be afraid to send units into areas with 25% risk. On the first few turns aim for capturing an Apartment and School. On my final win, I couldn't find either one within 3 squares around me, so if you can't find it, turn something into one.
Once you're established, just aim for a victory condition. I recommend finding the graveyard or city hall since that's much faster than the research or capture all squares victory conditions.