It seems to me that the big difference between 2nd league and 3th league for a very long time now is the knowledge of the chainrule.
I seem to walkover 3th league every 2 championships and then relegate back, because I can win easily if my opponent doesn't know the chainrule and loose in all other cases much to often.
One insight that made me start winning many more games was that it's a lot easier to change the chain count by joining small regions together than it is to cut even a really large region in half. If a box already has two of its edges filled in then either it will eventually become part of a chain or you opponent will have to sacrifice it. Try to make it so that you opponent has to pay to stop you joining the regions together.