How to beat impossible mode:
1. When the opponent has spawned the first wave of enemies, use the meteor shower. This gives you enough money to buy an egg-shooter.
2. Train clubmen to defend the base, but make sure they encounter the enemy within range of your egg-shooter.
3. Keep using the meteor shower whenever it's ready. DO NOT evolve yet.
4. Once you reach 1200 gold, buy another cannon slot + egg-shooter. Continue spawning clubmen to keep the enemy at bay (still within range of your artillery). It is necessary to train cave men at a constant rate.
5. Once you reach 14000 gold AND 45000 exp (should happen almost simultaneously), evolve 3 levels to military level, sell one of your egg-shooters and build a dbl turret.
6. From here on you don't have to spawn soldiers at a constant rate. I recommend building 4 dbl turrets, evolve to the last level and replace each turret with ion cannons when you have the gold.
7. Lastly, save up 600000 gold and send 4 super soldiers.