Final answer:
Henry VIII established himself as King of Ireland in 1541 after an act of the Irish Parliament.
Step-by-step explanation:
The question asks who established themselves as King of Ireland in 1541. The answer is Henry VIII of England. During his reign, Henry VIII underwent a significant process to solidify his power, including separating England from the Roman Catholic Church and establishing the Church of England with the king as its head. In 1541, through an act of the Irish Parliament, Henry VIII declared himself King of Ireland, asserting royal control over Ireland which until then had been exercised through the feudal Lordship of Ireland.