This is the bulkified version of Non-Bulkified code

Bulkified Code.java

//Declaring initial list to hold list of child records for single update at last  
List<child__c> childUpdateList = new List<child__c>();  
//Child query is used to return both child and parent records in single query  
for(Parent__c parent: [SELECT Id,name,Status__c,(SELECT Id,Name,Parent__c, child_Status__c FROM Child__r)   
                       FROM Parent__c])      
{  
    if(parent.Status__c =='Completed')  
    {               
        //If parent status is completed child record status is changed and added into a list  
        for(child__c child:parent.Child__r)  
        {  
            child.child_status__c ='Completed';  
            childUpdateList.add(child);  
        }  
    }  
}  
//At the end if there are child records to be updated, it is updated  
if(!childUpdateList.isEmpty())  
{  
  update childUpdateList;     
}