I just played it and won first time on Android, and have done on iOS. I'll try and test the Mac version later if you still have problems (should be no different but pc/mac/linux do have a different setting internally which maybe has gone wrong).
From the start, I make sure I have 3 dyson trees and 1 defence tree per asteroid until I find safer corner asteroids. Once I had my first 2 asteroids fully planted, I explored quite rapidly and carefully. I use flowers to create laser mines as quick as possible, and explore with those. When not exploring, I keep enemy numbers down using them.
When taking enemy asteroids, I pick the ones with as many dyson trees as possible so I get them cheaply, and I invade them laser mine first.
I didn't bother with places which had > 1 defense tree.
If attacking defense trees, you really want to get young, small asteroid ones. Larger ones will take out too many seedlings unless you have good quality super seedlings.
Sometimes Eufloria can make it tough right from the start - that's the procedural nature of the game. It doesn't happen often, but every now and again you get a tough start layout. I think it happened once to me on 200 - at least, I remember losing the level once. I may have just played it badly.