Biggs was commissioned lieutenant on 7 August 1761, had the cutter Folkestone 6 serving in home waters in 1768, and the cutter Grace 6 from 1769-71. He was promoted commander on 10 January 1771 and recommissioned the Favourite 16 at Portsmouth, in which he went out to the Leeward Islands in August before returning to pay her off in October 1775.
He was posted captain on 18 March 1778 and recommissioned the Lively 20, being attached to the Channel fleet and cruising off Brest in order to keep the commander-in-chief informed of the French fleet’s manoeuvres prior to the Battle of Ushant on 27 July 1778 Unfortunately his command was captured by the French fleet off Brest on 9 July, although he refused to strike his colours until fired into by the frigate Iphigénie 32. The Lively was subsequently recaptured by the Perseverance 36, Captain Skeffington Lutwidge, on 29 July 1781.
From early 1780 Biggs commanded the Amphitrite 24, going out to North America in May with Rear-Admiral Thomas Graves’ squadron and taking a huge number of enemy privateers and ships including the brig Amsterdam on 19 October 1781, which vessel was bought into the Navy. The Amphitrite remained on the American station until the end of the war and was eventually paid off in January 1784.
Biggs did not serve again thereafter but in due course was promoted rear-admiral on 1 June 1795 and vice-admiral on 24 February 1799.
He died at his residence in Catisfield, Hampshire, on 11 July 1803.