In the Battle of Martinique, on 18 December 1779, Annibal single-handedly engaged seven ships of the line to protect a convoy, and withdrew without anyone being killed aboard.

[3] At the Battle of Porto Praya, her captain, Achille de Trémigon, failed to understand Suffren's intentions to illegally attack the British fleet without consideration for the Portuguese neutrality, and followed Héros into the harbour unprepared for battle.

Trémigon was killed by a cannonball that struck his leg, and First Officer Morard de Galles assumed command.

After the battle, Suffren gave command of Annibal to Captain Bernard Boudin de Tromelin.

She was commissioned into the Royal Navy as the third-rate HMS Achille, retaining the French spelling of the name.