A chance Meeting on the Sea of Atlas

Tradescant at London Archives

Head to Santo Domingo and speak to Tradescant at docks

Head out straight South and click on merchant ship with quest mark

Defeat or retreat from battle with Ancient Galley and return to Santo Domingo

Speak to Tradescant inside, then again at the tavern

Find Tradescant East of the shipyard and speak to him again

After being released from jail, head to docks and equip battleship, head to San Juan and speak to Baltazar just north of the port. 2 battles will ensue, the Ghost of Atlantis and then Morgan's fleet

After defeating both, head to San Juan and speak to Tradescant, Wallenstein and Baltazar inside

Quest completed :)