What evidence is there that crusaders or Christians used "Deus Vult" as a battlecry? Are there even any recorded battlecries in history that we know of?
There were battle cries during the Middle Ages. For example, Antoine de La Sale's Le petit Jehan de Saintré—a sort of late medieval book of aristocratic behavior—proceeds almost as if an encylopedia mentioning the various regions of France, their arms, nicknames, and battle cries. All of these were idiosyncratic to the region or lordship in question. These most likely were used in ceremony or in the moments before battle was joined. In an example from the thirteenth century, Joinville narrates how while on the Nile the Lord Walter of Autreche, having mounted his horse and resplendent in his finest arms, charged at the enemy from his tent shouting "Châtillon!" Walter then falls off his horse and dies to the Egyptian army. You, the reader or listener, are meant to think Walter was foolish, drinking wine and suiting up on his pavilion before charging the enemy alone; but, it also lets us see how such phrases may have been used.
A battle cry—defined here as a cry employed in battle—, however, was more frequently used as a marker of identification among combatants. For example, in his chronicle of the thirteenth-century Ibelin family, Philip of Novara recounts how in a fight outside the castle of Dieudamour a brave Tuscan knight was killed by his allies because he could not say the King's password, vaillance, but instead cried out baillance. A poor French accent could get you killed amidst the chaos of the battlefield.
Historians and cultural critics have often named Deus Vult the battle cry of the crusades since it is the phrased shouted by those listening to Pope Urban II's speech outside Clermont in 1095. This is attested in many of the accounts of Urban's speech, and is one of the few things the competing sources agree on. But, there are reasons why this latin phrase is not likely to have been frequently employed. First among many is that it is in latin. Knights would have known some latin, and certainly would have been able to recite some liturgical, biblical, or otherwise colloquial phrases as we do with other languages today. It is even likely that some, limited number of nobles knew how to read and write in Latin. But, particularly as the twelfth century went on, the use of the vernacular was far more common. Whatever battle cry people would use would almost certainly be in French, Middle High German, etc.
A final example to demonstrate this fact would again come from Joinville, who when writing his history of the Seventh Crusade in his later years remembered the French knights on the Nile shouting not Deus Vult, but Montjoie. Montjoie is a French word recorded across multiple chanson de geste as a rallying cry of legendary medieval heroes such as William of Orange and Roland. It is best left untranslated as its meaning remains contested among scholars.