Answer taken from Islamqa.info’s summary of their own answer.
https://islamqa.info/ar/answers/239755
Summary of the answer:
This Hadith is weak from all its chains of narration together- except for the aforementioned Hadith of Anas bin Malik (in the detailed answer) which is very weak- and we can’t say that it raises to the level of Hasan (acceptable) because of the many paths of narration. (I.e. the narrations are extremely weak such that adding up all of them still renders it too weak.)
It was declared weak by Al-Albani in his book, ‘Al-Irwa Al-Ghaleel Fee Manar As-Sabeel (74)’, and similarly by Shaikh Abdul Qadir Al-Arnauut in his Ta’leeq (comments and checking) on Al-Adhkar (of Imam An-Nawawi) (p.304).
But this Dua has been proven generally from the Prophet ﷺ without limiting it to ‘looking into the mirror’. It was narrated by Ahmad (24392), Abu Ya’la (5075), At-Tayalisi (372), Al-Bayhaqi in Ash-Shuab (8183) from Aisha (رضي الله عنها).
It was narrated by ‘Aisha (رضي الله عنها) that she said, that the Prophet ﷺ used to say, “Oh Allah, as you have beautified me, beautify my character.”
It was authenticated by the redactors of Musnad Ahmad, similarly it was authenticated (Sahih) by Al-Albani in Saheeh Al-Jami’ As-Sagheer (1307). And Allah knows the best.
The Dua in Arabic:
اللهُمَّ أَحْسَنْتَ خَلْقِي ، فَأَحْسِنْ خُلُقِي.
Allahumma ahsanta khalqi fa-ahsin khuluqi.
Translated by Abu Muaaz Mohammed bin Thajammul Hussain Manna.
Saheehus-Seerah 