The Approval process information is held in the following Objects:
ProcessInstanceHistory is not exposed via the API. The ProcessInstanceStep stores each step of an Approval Process and is available via the API, which means that it can be accessed via dataloader.
The fields available in the ApprovalProcessStep are:
Id - the unique identifier for each entry in the ProcessInstanceStep object
ProcessInstanceId - the iD of the ProcessInstance that this approval step belongs to (ProcessInstance - Represents an instance of a single, end-to-end approval process.)
StepStatus - The current status of this approval step, for example Pending or Approved.
If the approval step requires unanimous approval and one approver rejects the request, the value of this field for the other approvers changes to NoResponse. Likewise, if approval is based on the first response and an approver responds, the value of this field for the other approvers changes to NoResponse.
OriginalActorId - ID of the user who was originally assigned to this approval step.
ActorId - ID of the user who is currently assigned to this approval step.
Comments - Limited to 4,000 bytes.
To access this object via dataloader, make sure to check the box titled "Show All Salesforce Objects" during the Object selection step.