Having passed his lieutenant’s examination on 17 February 1759, Biggs was eventually commissioned lieutenant on 7 August 1761. From 27 January 1768 he commanded the cutter Folkestone 6, serving in home waters, and thereafter he had the cutter Grace 6 from 20 July. He was promoted commander on 10 January 1771, being one of many officers advanced on that date, and later in the year he recommissioned the sloop Favourite 16 at Portsmouth. At the end of August, he took this vessel out to the Leeward Islands before returning to England in the summer of 1775 to pay her off in October.
After a spell as the regulating captain at Cowes, he was posted captain on 18 March 1778 and recommissioned the sixth rate Lively 20 at Sheerness, being sent to cruise off Brest in June in order to keep the commander-in-chief of the Grand Fleet, Admiral Hon. Augustus Keppel, appraised of the French fleet’s manoeuvres prior to the Battle of Ushant on 27 July. Unfortunately, his command was run down by the French fleet off Brest on 9 July, although he refused to strike his colours until fired into by the frigate Iphigénie 32. Various newspapers reported that he lost thirteen men killed and twenty-two wounded in this incident, even though the Lively’s colours were struck after receiving just a single broadside. Biggs was taken with his officers on parole to Guingamp in Brittany, where he was forbidden to stray beyond a mile from the town. Having been exchanged in early 1780, he was court-martialled for the loss of the Lively aboard the Prince of Wales 74 at Portsmouth on 31 January and was honourably acquitted.
From 15 March 1780 he commanded the small frigate Amphitrite 24, departing Portsmouth for North America on 10 April with Rear-Admiral Thomas Graves’ squadron, and capturing a huge number of enemy privateers and ships in addition to earning the respect of the loyalist population for taking the war to the enemy with such ardour. After being sent to Boston Bay, he took the privateer brig Amsterdam 10 on 19 October 1781, which vessel was bought into the Navy as the Observer 14. The Amphitrite remained on the North American station until the end of the war, and after returning to Portsmouth from the West Indies with several other men of war on 14 July 1783, she was eventually paid off at Woolwich in January 1784.
Biggs remained unemployed for the next eleven years before briefly being called back to duty in the third year of the French Revolutionary War when appointed on 10 May 1795 to the French prize Commerce de Marseilles 120, which had been commandeered following the evacuation of Toulon in 1793, and which was ready for sea at Spithead. In the event he barely held this commission for a month, for in line with his seniority he was promoted rear-admiral on 1 June 1795. Remaining on the beach, he was further promoted vice-admiral on 24 February 1799.
Admiral Biggs died at his residence in Catisfield, Hampshire, on 11 July 1803.