In YARN, ApplicationMaster is a critical process that optimizes the use of resources across the cluster. It negotiates resources with the ResourceManager and manages the execution of tasks on individual nodes.

In advanced Hadoop deployments, batch processing is often optimized for performance by leveraging in-memory processing. This involves storing intermediate data in memory rather than writing it to disk, reducing the time needed for data access and improving overall processing speed. In-memory processing is a key strategy for enhancing the performance of batch processing jobs in Hadoop.

DistCp (Distributed Copy) is commonly used in Hadoop for incremental backups of HDFS data. It efficiently copies large amounts of data between clusters and supports the incremental copying of only the changed data, reducing the overhead of full backups.

Adjusting the 'shuffle' parameter in Hadoop can significantly improve the performance of MapReduce jobs. The shuffle phase involves the movement of intermediate data between the Map and Reduce tasks, and tuning this parameter can optimize the data transfer process.

The integration of Apache Pig with Apache Spark allows for enhanced data processing and analysis in Hadoop. Apache Spark provides in-memory processing and advanced analytics capabilities, complementing Pig's data processing capabilities and enabling more sophisticated data workflows.

In complex data transformation tasks involving multiple data sources, Apache Sqoop is a preferred approach. Sqoop facilitates efficient and accurate data transfer between Hadoop and relational databases, ensuring seamless integration of diverse data sources for comprehensive transformations.

Load Balancing is key to maintaining the efficiency of a Hadoop cluster as data volume grows. It ensures that the computational load is evenly distributed among the nodes in the cluster, preventing any single node from becoming a bottleneck.

MapReduce handles large datasets in a distributed computing environment through data partitioning. The input data is divided into smaller chunks, and each chunk is processed independently by different nodes in the cluster. This parallel processing enhances the overall efficiency of data analysis.

Replication is the process by which HDFS ensures that each data block has the correct number of replicas. This helps in achieving fault tolerance by storing multiple copies of data across different nodes in the cluster.

In Cascading, a 'Tap' represents an input source or output sink in the data processing pipeline. It serves as a connection to external data sources or destinations, allowing data to flow through the Cascading application for processing.