Fantastic looking game - beautiful minis and table - but, as you mention, that scenario does seem broken. I'm not familiar with Tactica rules, but I'm surprised that 'mud' is only an optional rule for this battle.
I highly recommend Agincourt A New History by Prof. Anne Curry. As well as the traditional narrative of the French riding through a quagmire under a constant hail of arrows, she also argues that the French cavalry charge was probably undercooked, with insufficient numbers to overwhelm the English lines, that the foot slogging men-at-arms, disrupted by the retreating cavalry and advancing through treacle, would have been exhausted by the time they reached the English lines, and that the French archers and a large part of the French reserve failed to engage at all. Ultimately, though, this battle really is about the topography and the ground conditions.