The nameship of a pair of "74's" ordered in 1795, Achille was built in Cleverley's yard at Gravesend where she was laid down in October the same year. Launched on 16th April 1798, she was measured at 1,916 tons, was 182 feet in length and mounted 74-guns including a main armament of 30-32pdrs. on her gundeck.

First employed with the Channel Fleet and later in the blockade of Brest and Rochefort, she was found to be in serious need of repair in 1802 and was laid-up for all of 1803 whilst the necessary work was carried out. Back in the Channel Fleet in 1805, she was present at Trafalgar in Lord Collingwood's lee column and followed Colossus into action. Although engaging several of the enemy during the battle, her duel with the French Berwick lasted over an hour before the latter finally surrendered to Achille's Captain King after a bitter action resulting in heavy casualties and damage to both ships. Later operations included the expedition to Walcheren and the blockades of Flushing and Cadiz, and she ended the War having captured a sizeable amount of enemy tonnage. Thereafter laid-up for most of the first half of the nineteenth century, she was finally broken up in 1865 and her timbers sold for £3,600.