Grading: Its chain is sahih.
Technical note / Defect ('illah): Ibn Uyaynah (Sufyan) has three chains for this hadith, one of which is this, as will be explained below. Al-Sha'bi is Amir bin Sharahil.

Reference / Source: A group narrated it from Sufyan bin Uyaynah with this same chain, among them Abd al-Razzaq (as in the narration of the author (al-Hakim), and it is in "al-Musannaf" 6403); Abu Ubaydullah al-Makhzumi Sa'id bin Abd al-Rahman (in Abu al-Qasim al-Baghawi's "Mu'jam al-Sahabah" 987); and Muhammad bin al-Sabbah (in Abu Nu'aym's "Ma'rifat al-Sahabah" 3282).

Corroborating chains and supporting reports: A group of hafiz (master) scholars corroborated Ibn Uyaynah on this chain. Among them are Muhammad bin Yazid al-Wasiti (in al-Shafi'i's "al-Umm" 8/ 413); Yazid bin Harun and Ya'la bin Ubayd (in Ibn Sa'd's "al-Tabaqat" 3/ 438); Abu Awanah (in al-Bukhari's "al-Tarikh al-Awsat" 1/ 562); Waki' (in Ibn Abi Shaybah 3/ 305); and Yahya al-Qattan (in al-Tahawi's "Sharh Ma'ani al-Athar" 1/ 496).

Reference / Source: Al-Bukhari narrated it in his "Sahih" (4004) via Muhammad bin Abbad from Ibn Uyaynah, who said: Ibn al-Asbahani conveyed this hadith to us; he heard it from Ibn Ma'qil that Ali led the funeral prayer (said the takbir) over Sahl bin Hunayf and said: "He was present at Badr."
Note / Clarification: Al-Bukhari did not mention the number of takbirs here, although he narrated this same report with this very chain in "al-Tarikh al-Awsat" (1/ 559) and said there: "He said six takbirs." Al-Bukhari also narrated it in "al-Tarikh al-Kabir" (4/ 97) via Shu'bah bin al-Hajjaj from Ibn al-Asbahani, and said there too: "He said six takbirs over him." See Ibn Hajar's "Fath al-Bari" (12/ 84).

Important point: Ibn Uyaynah also has a third chain for it, from Yazid bin Abi Ziyad, from Abdullah bin Ma'qil; it is in Abd al-Razzaq (6399), al-Bukhari's "al-Tarikh al-Awsat" (1/ 559) and elsewhere.

Important point: Abu Mas'ud al-Dimashqi said (as al-Mizzi quoted from him in "Tuhfat al-Ashraf" 7/ 415-416): "This is among what Ibn Uyaynah first heard from Isma'il bin Abi Khalid, from al-Sha'bi, from Abdullah bin Ma'qil; then he later heard it from Ibn al-Asbahani, from Ibn Ma'qil."