The context gives no clue - there are no grounds for preferring either. Almost all combinations are possible for the three verbs, except that if 'entered' is past simple, 'apologized' must also be. As there is no extra merit in using the past perfect here, I would use past simple throughout, on the basis that a simpler form is preferable to a more complex one, all else being equal. Your spelling of 'apologized' suggests you are studying American English, which has a bias towards using the simple past rather than perfect tenses anyway, giving even more reason to use it.

"Before the second chicken had been cooked..." and then the rest in past simple or past perfect. That said, there isn't much difference and past simple would be quite clear, particularly as you have the time marker "before".