It depends whether the answer is from a Shia view or Sunni view. From Shia view, he had no achievements because he was not qualified for the position of Caliphate and, in fact, stole this position from Imam Ali a.s. and so he destroyed Islam and made Bidats (for example making Taraweeh prayer by Jamaat and banning the Mutah ,...)
Caliph Omar's greatest achievements were the expansion the Islamic Caliphate to Egypt, the Levant, to Mesopotamia, to Persia, and to eastern Anatolia.
Yahya ibn Idris ibn Umar died in 917.
Umar ibn Hafsun died in 918.
Umar ibn Hafsun was born in 850.
Yahya ibn Umar died in 864.
Sayf ibn Umar died in 796.
Ali ibn Umar died in 883.
Al-Qadi Aqib ibn Mahmud ibn Umar died in 1627.
Al-Qadi Aqib ibn Mahmud ibn Umar was born in 1556.
Umar Ibn Muhammad of Borno died in 1967.
Umar Ibn Abi Rabi'ah was born in 644.
Abû 'Umar ibn Sa'îd died in 1287.
Expedition of Umar ibn al-Khatab happened in 628.