There are a total of 42 missions in total, and for this you need to complete any 35 of them. As well as the 'Campaign' and 'Campaign Challenge' modes, there are various other modes such as 'Grinder' and 'Super Grinder' (up to 99 waves), 'Poison Core' (a single core that kills enemies when returning) and 'Frozen Core' (single core that doesn't return). You can pretty much use your solution for the Campaign levels, and just tweak them to the challenge stipulations. For example, the Grinder and Super Grinder levels, use your solution but upgrade more towers and add towers for the later levels. For Poison Core, just use your original solution but maybe a few less upgrades as the returning cubes will kill enemies on it's way back.
As you have seven map modes that you don't need to do, I would recommend skipping the Frozen Core challenges in particular as they are really difficult, you basically cannot have a single cube get taken at all.
These are the tougher levels, although of course the choise is yours!
An excellent playlist of gold medals on all maps and modes can be found here. If you decide to try going alone, there are many different ways to complete each and every level in this game to a gold medal standard. Remember to always ensure that the aliens are taking the longest possible routes so you have more time to kill them. If you make a mistake, you can hit to go to your last checkpoint; and hit it multiple times to go back further.