I don't think the phrase is formal and academic enough, but I can't think of a word to replace it.
I want to say something like this: The two frogs both agreed that they needed to fight, but their fighting strategies "couldn't have been more different."
Best Answer
There are a number of modifiers to "different" which will work:
etc.
Depending on the sense, you could go for opposite.
Another single word is diametric, one sense of which is completely opposed. Or, in that same vein, maybe antithetical, which is being in direct and unequivocal opposition.