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.

In a Hadoop cluster, the ResourceManager is typically scaled first for performance enhancement. It manages resource allocation and scheduling, and scaling it ensures better coordination of resources, leading to improved job execution and overall cluster performance.

In the context of handling memory-intensive applications, garbage collection is crucial in advanced Hadoop tuning. Efficient garbage collection helps reclaim memory occupied by unused objects, preventing memory leaks and enhancing the overall performance of Hadoop applications.

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.

DBInputFormat is ideal for processing structured data stored in databases in Hadoop. It allows Hadoop MapReduce jobs to read data from relational database tables, providing a convenient way to integrate Hadoop with structured data sources.