KeywordsManager.SetTaxKeywordValue.cs

using (var ctx = new ClientContext(webUri))
{
    ctx.Credentials = CreateSPOCredentials(userName, password);
    var list = ctx.Web.Lists.GetByTitle(listTitle);
    var item = list.GetItemById(itemId);
    KeywordsManager.SetTaxKeywordValue(item,new []{"2013","2010"});
    item.Update();
    ctx.ExecuteQuery();
}

public static SharePointOnlineCredentials CreateSPOCredentials(string userName,string password)
{
    var securePassword = new SecureString();
    foreach (var ch in password)
    {
        securePassword.AppendChar(ch);
    }
    return new SharePointOnlineCredentials(userName, securePassword);
}