World first FIFA hatrick

1930 FIFA World Cup records the world's first FIFA World Cup hat trick in a match held between the United States and Paraguay. The match played on July 17 at Estadio Parque Central, Montevideo ended with a win for the United States with three goals to nil. Bert Patenaude, a forward for the United States netted the three goals at 10 minutes, 15 minutes and 50 minutes of the game. United States was defeated in the semi-final by Argentina and Patenaude had a total of four goals in the tournament. 

Patenaude had to wait till 2006 to have his confirmation of his feat, 32 years after his death. The controversy of the second goal was finally approved by FIFA to Patenaude’s credit.

World's first women cricketer to be given retired out

“In cricket, a batsman retires out if he retires without the umpire's permission, and does not have the permission of the opposition captain to resume his innings. This occasionally happens in friendly or practice matches, for instance English county sides against University Centres of Cricketing Excellence. Although it is not considered to be a dismissal in the context of a cricket match, it is considered a dismissal for the purposes of calculating a batting average.” (Wikipedia)

In International Women's cricket, the only instance of an unusual dismissal came in a One Day International match between Sri Lanka and the West Indies in April 2010. Sri Lanka wicket-keeper Dilani Manodara was retired out due to her slow scoring rate in her team's first innings, having taken 70 minutes and 39 balls to score 8 runs.