Requirement:

Mark First Response Milestone as completed when the agent changes the status of the Case from New to Working.

Note:

IsCompleted field in CaseMilestone is not Writeable/Editable.

So, this cannot be updated.

But, to update the IsCompleted field, update the CompletionDate field. Once the CompletionDate field is updated, the IsCompleted flag will be updated. 

Sample Trigger:

trigger CaseTrigger on Case ( after update ) {

    Set < Id > setCaseIds = new Set < Id >();

    for ( Case objCase : trigger.new ) {
    
        if ( objCase.Status == 'Working' && trigger.oldMap.get( objCase.Id ).Status == 'New' ) {
        
            setCaseIds.add( objCase.Id );
        }        
    
    }
    
    if ( setCaseIds.size() > 0 ) {
    
        List < CaseMilestone > listCaseMilestones = new List < CaseMilestone >();
        
        for ( CaseMilestone objCM : [ SELECT Id, CompletionDate FROM CaseMilestone WHERE CaseId IN: setCaseIds AND MilestoneType.Name = 'First Response' ] ) {
            
            objCM.CompletionDate = System.now();
            listCaseMilestones.add( objCM );
            
        }
        
        if ( listCaseMilestones.size() > 0 ) {
        
            update listCaseMilestones;
            
        }
    
    }

}