In 1273, the key battles involving the figures Bachaler and Kemény are not explicitly documented in historical texts available up to October 2023. However, the general historical context of that period includes conflicts related to the power struggles within the Kingdom of Hungary and surrounding regions. During the 13th century, Hungary was often involved in internal conflicts and external threats, such as the Mongol invasions earlier in the century and subsequent power struggles among Hungarian nobility.

If Bachaler and Kemény were involved in any specific battles during 1273, they would likely be related to these broader conflicts. For more precise information, consulting specialized historical sources or records from the Kingdom of Hungary during that time would be necessary.