All of the Takbīrs (saying Allāhu Akbar), except the opening Takbīr (which is a pillar (translator’s addition)).
These are also called Takbīr al intiqāl (Takbīr for moving from one position to another) because Ibn ‘Abbās said, “I saw the Prophet (May Allāh praise him and Peace be upon him) say Allāhu Akbar every time he went up or down and every time he stood or sat. The Prophet (May Allāh praise him and Peace be upon him) did that until he died, and he (May Allāh praise him and Peace be upon him) said, “Pray as you have seen me pray.” [Authenticated by Al Albānī in ‘Ṣaḥīḥ Al Tirmidhī’ number 208].
Saying “Sami’a Allāhu liman ḥamidah” (Allāh hears and answers those who praise him) is obligatory for the imam and for anybody praying individually. This is because Abū Hurayrah (may Allāh be pleased with him) said, “Allāh’s Messenger (May Allāh praise him and Peace be upon him) used to say Allāhu Akbar when he stood up and when he went in rukū’ (bowing). Then he said Sami’a Allāhu liman ḥamidah when he straightened up from rukū’. Then while standing, he would say Rabbanā wa laka al ḥamd (Our Lord, to You belongs all praise). There is also the ḥadīth of Abū Mūsā Al Ash’arī that contains the wording “And when he says Sami’a Allāhu liman ḥamida, say Rabbanā laka al ḥamd (Our Lord, to You belongs all praise).” [Reported by Imam Muslim no. 404 and Imam Aḥmad (4/399)].
Saying “Subḥāna Rabbī Al ‘Aẓīm” (Free be My Lord the Almighty from all imperfections) in rukū’.
Saying “Subḥāna Rabbī Al A‘lā” (Free be My Lord the Most High from all imperfections) at least one during each prostration. This is because in his ḥadīth, Ḥudhayfah Ibn Yamān said, “He (meaning the Prophet (May Allāh praise him and Peace be upon him)) used to say “Subḥāna Rabbī Al ‘Aẓīm” (Free be My Lord the Almighty from all imperfections) in rukū’” (bowing) and “Subḥāna Rabbī Al A‘lā” (Free be My Lord the Most High from all imperfections) in prostration” [Authenticated by Al Albānī in Ṣaḥīḥ Al Nisā`ī no. 1097].
Saying “Rabbighfir lī” (My Lord forgive me) between prostrations; this is because the Ḥadīth of Ḥudhayfah which mentions that the Prophet (May Allāh praise him and Peace be upon him)) used to say “Rabbighfir lī, “Rabbighfir lī” between prostrations [Authenticated by Al-Albāni in Al-Irwā` 9 no. 335].
The first tashahhud, unless the imam stands up out of forgetfulness- in which case, it is not obligatory because he must follow the imam. This is because when the Prophet (May Allāh praise him and Peace be upon him) forgot the first one, he did not return to it, but made up for it with sujūd al sahw (prostration of forgetfulness). [Reported by Imam Al Bukhārī 1230].
Sitting for the first tashahhud; This is because of the marfū’ (attributed to the Prophet (May Allāh praise him and Peace be upon him)) ḥadīth of Ibn Mas’ūd which says, “When you sit every two rak’ah (units of prayer) say “Al-tahiyyātu lillāh”” [Authenticated by Al-Albāni in Al-Irwā` /336]