It is often taught in History books that the Mughals had been the apex predators in the military history of India. This article details some of the battles fought at Delhi in which the Mughals have been a party.
1. 7th October, 1556: Hemchandra (Hemu) vs Mughals
When Humayun’s Governor of Agra saw Hemu’s forces approaching, he fled to Delhi. In his pursuit, Hemu reached Tughlaqabad. Tardi Beg, Mughal Governor of Delhi faced him.
Due to the clever tactics of Hemu, he won the battle as the Mughal officers fled away in terror. He then took possession of Delhi. 
2. 30th March, 1737: Marathas vs Mughals
Peshwa Baji Rao’s forces repulsed with heavy losses a Mughal attack of 8,000 troops led by Mir Hasan Khan.
Baji Rao could have acquired control of the capital with an assault but thought it prudent to decamp from Delhi. 
3. May, 1753: Jats vs Mughals
It was a part of Safdar Jung’s rebellion. Suraj Mal and Rajendra Giri, on Safdar Jung’s insistence, attacked Old Delhi on 9th. What followed was a total devastation for the Mughals which continued for several days. There were several battles fought in this struggle resulting in several victories for the Jats and Safdar Jung. At its peak, on 17th May, the Kohtila of Firuz Shah was captured.
They moved away south of Delhi after a series of stalemates from 5th June onwards. Safdar Jung’s rebellion continued till November when peace he made peace at Ballabhgarh. 
4. 11th August – 3rd September, 1757: Marathas vs Mughals
The real master of Delhi government after Abdali’s exploits was Najib. He was appointed by the Mughal Emperor. Imad, the Wazir, conspired to oust him.
Long story short, Marathas attacked the city from several sides with Raghunath Rao and Malharrao Holkar leading them. ‘Thus Delhi and its Sovereign once again exchanged one master for another.’ Najib was ousted and Imad gained control. 
5. November, 1764 – February, 1765: Jats vs Mughals
Jawahar Singh attacked Delhi to avenge his father’s death. He availed help from the Marathas, Sikhs and some Naga Sanniyasis. The siege continued till February. People of Delhi begged for food in the Jat camp or migrated elsewhere. In February 1765, a treaty was signed on payment of Rs. 60 Lakhs as war indemnity.  
6. February, 1771: Marathas vs Mughals
On 9th February, Marathas bombed the city from four sides and established their control the next day. Then, they agreed to install Shah Alam as their puppet after securing a compensation of 40 lakh rupees. 
 Jadunath Sarkar (1960), Military History of India, p. 67.
 J. L. Mehta (2005), Advanced Study in History of Modern India 1707-1813, p. 117.
 Jadunath Sarkar (1964), Fall of the Mughal Empire, Vol. 1, pp. 217-315.
 Jadunath Sarkar (1934), Fall of the Mughal Empire, Vol. 2.
 Lt. Ram Saroop Joon (1967), History of the Jats, p. 167.