What the heck is an RTA

Real Time Attack, so a stopwatch timing of the run. Check any video and you'll see a timer displayed next to it. It starts from selecting the cup to crossing the finish line on the last lap of the last track of the cup.

Just for reference, IGT is the opposite; the in game timing of a run. For example when you finish a time trial, the game shows the time you got: that's IGT or In-Game Time.