In reading the posts on this subject and my own experiences i have come to the preliminary conclusion that
1. the health of the boss is exclusively based on your level and has nothing to do with your actual attack force. They multiply your level with a fixed amount of allies (i assume 2.5 per level) and multiply this further with a fixed amount of units (i assume 4 per ally) and multyply that further with a high density number (in my rough calculations this seems to be 400 but this is definitely not accurate). So when you are level 200 this would lead to 200 x 2.5 allies x 4 units x 400 average virtual attackforce = 800.000 standard boss health. Finally, they will use a variable multiplier depending on the level of the boss. I do not know yet what this multiplier is but for level 30 it could be as high as 13.
2. To beat the boss without gold up to level 30 is possible only if you fight with the highest possible average density.
This also explains why lower levels can kill the boss a bit easier as some of them can maintain a higher density than the higher level players. E.g a level 2 player who purchases 20 units with say 400 attack force will problably have no problem in killing the boss up to level 30 without purchasing gold.
I am pretty sure the above formula is correct, we only need to determine the correct multipliers. This is however easy to establish if you guys provide some data. The only thing i need is your level, the level of any boss you have beaten and the amount of health he had at that level. Please be as accurate as possible in determining his health. This is not that easy as they do not give you the amount of his healthbar so you need to be creative .