Here is the code for the Batch class: 

global class SmsCounterBatch implements Database.Batchable<sObject> {

	global Database.QueryLocator start(Database.BatchableContext BC) {
		return Database.getQueryLocator([
			SELECT 
				Id, Total_SMS_Delivered__c, Total_SMS_Failed__c, Total_SMS_Sent__c, 
				(
					SELECT Id, SMS_Delivery_Status__c 
					FROM ActivityHistories 
					WHERE (ActivityType = 'SMS') AND (Status = 'Completed')
				) 
			FROM Campaign 
			WHERE (IsActive = TRUE) AND (EndDate >= TODAY) 
			ORDER BY LastModifiedDate DESC
		]);
	}

   	global void execute(Database.BatchableContext BC, List<Campaign> scope) {
   		List<Campaign> campaignToUpdate = new List<Campaign>();

		for(Campaign campaign : scope) {
			if(!campaign.ActivityHistories.isEmpty()) {
				campaign.Total_SMS_Delivered__c = 0;
				campaign.Total_SMS_Failed__c = 0;
				campaign.Total_SMS_Sent__c = 0;

				for(ActivityHistory record : campaign.ActivityHistories) {
					if(record.SMS_Delivery_Status__c == 'Delivered') campaign.Total_SMS_Delivered__c++;
					else if(record.SMS_Delivery_Status__c == 'OK') campaign.Total_SMS_Sent__c++;
					else campaign.Total_SMS_Failed__c++;
				}

				campaignToUpdate.add(campaign);
			}
		}

		if(!campaignToUpdate.isEmpty()) update campaignToUpdate;
	}
	
	global void finish(Database.BatchableContext BC) {  }
}

And currently, I only figured out this testing class:

@isTest(SeeAllData=true) 
public class SmsCounterBatchTest {

    @IsTest public static void couterBatchTestMethod() {
    	
    	Campaign cam1 = new Campaign ();
        cam1.Name = 'Test Campaign 1';
        cam1.IsActive = True;
        cam1.Total_SMS_Delivered__c = 0;
        cam1.Total_SMS_Sent__c = 0;
        cam1.Total_SMS_Failed__c = 0;
        
    	Insert cam1;
    	
    	Campaign cam2 = new Campaign();
        cam2.Name = 'Test Campaign 2';
        cam2.IsActive = True;
        cam2.Total_SMS_Delivered__c = 0;
        cam2.Total_SMS_Sent__c = 0;
        cam2.Total_SMS_Failed__c = 0;
        
    	Insert cam2;
        Contact c = new Contact();
        c.LastName = 'Test Account';

        insert c;
        
        SMS__c sms = new SMS__C();
        sms.Campaign__c = cam1.Id;
        sms.Delivery_Status__c = 'Delivered';
        sms.Message__c = 'Test Message';
        sms.Recipient__c = c.Id;
        sms.Transaction_ID__c = '1b9f8ac8eb75494e80f1474aeb61d93d';
        
        insert sms;
        List<Campaign> campaignList = [SELECT Id, Total_SMS_Delivered__c, Total_SMS_Failed__c, Total_SMS_Sent__c, 
				(
					SELECT Id, SMS_Delivery_Status__c 
					FROM ActivityHistories 
					WHERE (ActivityType = 'SMS') AND (Status = 'Completed')
				) 
			FROM Campaign 
			WHERE (IsActive = TRUE)];
        if(!campaignList.isEmpty()) {

        cam1.Total_SMS_Delivered__c = 0;
        cam1.Total_SMS_Sent__c = 0;
        cam1.Total_SMS_Failed__c = 0;
        }
        update cam1;
        

        Test.StartTest();

        SmsCounterBatch counterBatch = new SmsCounterBatch();
     	
     	Database.executeBatch(counterBatch);
	    
	    Test.StopTest();   
        System.AssertEquals(database.countquery('SELECT COUNT()'+' FROM SMS__c'), 21);
    }
}

And here the uncovered part of the Batch class:



I will appreciate any kind of help.
Thank you