Thanks JeffreyStevens for looking into this...

Below is the code sample as,

public static List < Id > getWorkItemIds(Id targetObjectId, Id actorId) {
	List < Id > workitemIdList = new List < Id > ();
	for (ProcessInstanceWorkitem workItem: [Select Id FROM ProcessInstanceWorkitem WHERE ProcessInstance.TargetObjectId = : targetObjectId AND ActorId = : actorId]) {
		workitemIdList.add(workItem.Id);
	}
	return workitemIdList;
}

public static Approval.ProcessResult processRequest(Id workItemId) {
	Approval.ProcessResult process_result = null;
	try {
		Approval.ProcessWorkitemRequest request = new Approval.ProcessWorkitemRequest();
		request.setAction('Approve');
		request.setWorkitemId(workItemId);
		request.setComments('Approved');
		process_result = Approval.process(request); 
	} catch(Exception ex) {
		ApexPages.addMessage(new ApexPages.message(ApexPages.Severity.ERROR, 'Error occurred while approving record');
	}
	return process_result;
}
  
public void approveRecord(targetId, actorId) {
	List<Id> workitemIds = getWorkItemIds(targetId, actorId);
	if(workitemIds != null && !workitemIds.isEmpty()) {
		for (ID wId: workItemIds) {
			Approval.ProcessResult pResult = processRequest(wId);
			if (process_result.isSuccess()) {
				// Record Updation Logic
				// Identify next level approver
				// Sending approval request to next level approver				
				// Send email notification
				// many more business logic...
			} else {
				ApexPages.addMessage(new ApexPages.message(ApexPages.Severity.ERROR, 'Error occurred while approving record');
			}
		}
	} else {
		ApexPages.addMessage(new ApexPages.message(ApexPages.Severity.ERROR, 'No Workitem exist for given targetId = ' + targetId);
	}
}

Need to write test class logic for approveRecord method.

Since I am not able to get WorkItem Ids as a result I am not able to test conditional block. 
Please let me know how can I perform INSERT operation on ProcessInstanceWorkitem to get data in query.
OR any other solution exist to write a better test class.

Thanks.