It takes lots of care to get a “highly nonlinear” problem to converge. If you can you reproduce your non-converging problem with a minimal working example (\backsim 30 lines of code or fewer), we can take a look.
If not, the following tips and tricks may help: Default absolute tolerance and relative tolerance
Also, try reducing the complexity of your problem until the Newton solver converges successfully so you can find the problematic portion of your formulation.