I can't get past the third challenge level. I've made a spreadsheet of all possible upgrades to damage and rate and it seems that in the price range I fail at, the best tower I can build is the Rocket tower with 40000 damage and 135 rate (cost $6715), but even that quickly loses to wave 42 of the challenge.

I get really close to being able to upgrade it to 60000 damage (MAX) but not quite.

My other idea would be maybe a combo between two towers would be more effective. However it seems impossible to afford two maxed out towers - the cheapest is the Tazer for $3360, but that has such short range I lose whenever I try it.

Any ideas?

Well I think just based on how freely the challenges can be altered, I don't believe all of them are doable.

But the ones that are proper named should be. I have not played the game seriously for aaaaages so I am not really sure. But probably especially if you did your maths right, maybe the way is laser damage? I think if you fine tune the laser chaining and upgrading of range and damage, it might be doable.

I will try looking for a solution for you online, there must be a thread hidden in the archives that mentiones this!