18 players have hit 4 homeruns in a game. 23 pitchers have pitched perfect games. 327 players have hit for the cycle but only 4 players have done it 3 times. A natural cycle is hitting a single, double, triple and home run in that order. It has only been done 5 times.
Only 15 players have ever had an unassisted triple play. None have been catchers but I can see how it would be theoretically possible but hugely improbable.
In 1964 Houston Colt 45's pitcher Ken Johnson became the only pitcher in major league history to lose a 9 inning complete game no hitter. Pete Rose scored the winning run.
In 1959 Pittsburgh Pirates pitcher Harvey Haddix pitch 12 perfect innings vs the Milwaukee Braves before losing in the 13th because of an error. https://www.mlb.com/cut4/harvey-haddix-threw-12-perfect-innings-and-lost/c-126504134
There has been only 1 post season perfect game ever. That by Don Larson of the Yankees vs the Brooklyn Don't in the 1956 World Series. https://baseballhall.org/discover/inside-pitch/larsen-perfect-game
Most RBIs In A Game,.. 12 Jim Bottomley, St. Louis, 1924 Mark Whiten, St. Louis, 1993 16 players have had 10 rbi's or more in a game http://www.baseball-almanac.com/recbooks/rb_rbi1.shtml
Close...The rarest feat in baseball is hitting the home run cycle (solo, 2R, 3R, GS). Its never been done in the majors. The only time in recorded baseball history that its been done was by Double A player Tyrone Horne in 1998 for the Arkansas Travelers. A softballer for the Arkansas Razorbacks (what is it about Ark?) did it earlier this year, but that doesn't count.