Aztec mentality would have been a big factor in how they fought. You can go deep into the influence of ritual sacrifice. Here's a bit about how warriors were raised, and then some details about battles.

Elite males could become either priests or warriors. The latter was preferred and prepared for as early as birth, when the midwife would meet the newborn with war-cries and ritual prayers. Then the umbilical cord would be "laid in the midst of the field of battle" by a warrior, "pledging the infant life to its violent end." Each boy would be surrounded by weaponry from the time of his naming ceremony, and if the Codex Mendoza is to be believed, "discipline, especially for males, would be tough, physical and immediate." By the age of ten the infant warrior would be covered in scars and burns, obtained from prescribed rituals and punishments. Many boys were bound naked in icy water or over a fire of chillis. They would visit the battlefield for the first time in a group at the age of 18, tempered and eager for prestige.

Any warrior who does not secure a captive after only two or three opportunities will be expelled from the caste and lose “not only the incomparable excitements of the warrior house, but also the chance of supplementing income, of social advancement, of local prestige.” These "soldiers of the sun" fight wearing skins of jaguars and skulls of eagles; colorful feathers adorn their small, round shields and headdresses. Without metallurgy, their weaponry consists of wood, stone, and obsidian. Most notable is the maquahuitl: a two-handed hybrid between club and sword fixed with sharp, obsidian shards. It is a weapon specialized for crippling and capturing unarmored enemies. For that same reason it was useless against Spanish Conquistadors.

I can post more about the religious aspect if you're interested.

[sorry, no page numbers]

David Carrasco. City of Sacrifice: The Aztec Empire and the Role of Violence in Civilization. Beacon Press, 2000.

Inga Clendinnen. Aztecs: An Interpretation. Cambridge University Press, 1995.

Manuel Aguilar-Moreno. Handbook to Life in the Aztec World. Oxford University Press, 2007.

Ross Hassig. Aztec Warfare: Imperial Expansion and Political Control. University of Oklahoma Press, 1995.

There's always room for discussion, but perhaps these topics from the Pre-Modern Non-Western Warfare of our FAQ will answer your inquiry.

• How were battles fought during the Flowery Wars involving the Aztecs, in terms of tactics, weaponry, etc.?

• Aztec Warfare