How to replicate information from an approval process.

Use table and row replication: 

Relationship 1
Table Relationship
What you have - Object with Approval Process
What you want - ProcessInstance

Relationship 2
Row Replication
What you have - ProcessInstance (from above relationship)
What you want - ProcessInstanceStep

 

We can replicate all the data in the Approval Process History. Though the data appears in a related list-style section, Salesforce stores this data as parent records (one for each approval) and child records (one for each stage of the approval).