• Created a checkbox field Is Shared and default is false. 
• Query on Case object where Is Shared = false (i.e: record not yet shared) and Query will return not shared records
• Query on Group object to get the Group Id. For now I used specific Group for sharing. 
• Iterate the list of Case records and creating CaseShare for the same and Updating the shared record Case.Is Shared to true. So next time our batch will not process this record. 

global class batchCaseUpdate implements Database.Batchable<sObject> {
    global Database.QueryLocator start(Database.BatchableContext BC) 
    {
        /*If you want you can add more condition based on your requirement. 
        Currently the condition will check the case is already assigned to any groups are not. Any one of case not assigned to group then it will execute the method */
        String query = 'SELECT Id FROM Case where Is_Shared__c = false';
        return Database.getQueryLocator(query);
    }
    global void execute(Database.BatchableContext BC, List<Case> lstCase) 
    {
        //To get the GroupId which we need to assign to Case.
        List<Group> lstGroup = new List<Group>([SELECT Id,DeveloperName FROM Group where DeveloperName = 'Case_Sharing']);        
        List<CaseShare> lstCaseShare = new List<CaseShare>();
        
        //If given groups are available in org then condition will execute else it won't exeute anything
        if(!lstGroup.isEmpty())
            for(Case objCase :  lstCase)
            {
                lstCaseShare.add(new CaseShare(CaseId = objCase.Id, UserOrGroupId = lstGroup[0].Id, CaseAccessLevel ='Edit'));
                objCase.Is_Shared__c = true;
            }
            
        Database.Insert(lstCaseShare, true);  
        Database.Update(lstCase, true);  
    }
    global void finish(Database.BatchableContext BC) 
    {
    
        
    }
}