Is it better in supplication to specify the request, or to ask for what is good in the matter? And if asking for what is good is better, then why did the Messenger of Allah, peace and blessings be upon him, pray for victory at Badr?

A servant is permitted to supplicate to Allah for whatever they wish regarding the affairs of this world and the Hereafter, as long as it does not involve sin, severing ties, or aggression. The Prophet, peace and blessings be upon him, used to supplicate for specific matters, as indicated by his supplication for the oppressed and against Mudar. Imam Malik affirmed the permissibility for a man to supplicate for all his needs of this world and the Hereafter during the prescribed prayers, whether standing, sitting, or prostrating. 'Urwah ibn al-Zubair even said, "Indeed, I supplicate to Allah for all my needs in prayer, even for salt." It has also been reported from Imam Ahmad that it is permissible to supplicate for the needs and pleasures of this world.