Terrapin Manip allows you to save time by controlling how many times you get punched by the 4 Terrapins in Bowser's Keep (if you do not manipulate the RNG you will get hit anywhere from 0 to 6 times).
This tech is not mandatory, don't reset over it if you are not getting sub 3 times.
1-punch manip (slow, easy-ish):
LackAttack24's Any% tutorial video includes an introduction and demonstration of a manip that will get you punched only 1 time.
0-punch manip (slow, easy-ish):
Alanim's 0-punch manip method has more waiting between attacks but safer input windows (and obviously, less punches).
You can download his emulator video and drag this video onto Snes9X running a Japanese SMRPG ROM and use frame advance to analyze it.
This is about as fast as the 1-punch manip.