Hold Start when selecting a course. You'll instead select a Mirrored version of it. There's not really much of a way to tell you've done this right until the stage loads.

POWER EDITION ONLY!
Hold Brake when selecting a course.
'Reverse' will show up at the bottom of the screen to let you know you've done it.
There is a way to drive the course backwards in Battle on the Edge though...
turn around when the race starts! Your pit crew will beg you to turn around, but eventually the big 'Reverse' banner will move to the bottom of the screen, and in
the Japanese version you'll hear Takenobu Mitsuyoshi yell "逆走だぁー!!" ("You're Driving Backwards!!"), signifying you're now running the race in reverse. Obviously, there's one very big difference between this and Power Edition's more 'legitimate' implementation though -
you're driving into oncoming traffic! This easter egg is actually a carry over from the original game, including the Mitsuyoshi shout.

If you're able to do this and actually finish the race, you're treated to a unique sight; the ending credits for the stage, despite the fact you technically finished last!

Hold Start when selecting a transmission to enable Time Attack mode.OK, this one isn't really hidden; the game literally tells you about it. But we might as well be thorough...
Hold Start during the "Gentlemen, Start Your Engines" screen.This toggles the vocalist opposite to the game's current default settings. The US region default is Dennis St James, while the JP default is Takenobu Mitsuyoshi.
This code's notable as with the US board region, it's actually the
only way to hear Mitsuyoshi's vocals - you can't change the vocalist setting in the Test Menu outside of Japan!
Apparently this was also supposed to change the announcer clip used when selecting the Challenge/Mix course in Power Edition too - in the Japanese version, you'll always hear Mitsuyoshi shout 'MIX!' when selecting it, and in the US version you'll always
hear Dennis St James say "Challenge";
but opposite voice clips exist for both versions!
POWER EDITION ONLY!
Hold one of the VR Buttons during the "Gentlemen, Start Your Engines" screen.
If you just can't get enough of the Beginner Course song (like me), why not just listen to it on every course? Each VR Button corresponds to a different song. The order's pretty obvious, but it's as follows:
VR1 - Slingshot ::
VR2 - I Can Do It ::
VR3 - Skyscraper Sequence ::
VR4 - Ending Medley
That last one's a bit odd - it literally just plays through the different 'Victory Lane' themes, and then once the last one ends, it's... just over. Could've popped an unused track in here, SEGA...
BATTLE ON THE EDGE ONLY!
Before starting the game, put the stick into Gear 1. At the Course Select, move into Gear 4. Before selecting a course, input the following VR Buttons: 1, 4, 2, 4, 1, 2, 2+3 (together), 1. You'll now have access to one of the best-kept secrets in all of gaming - the Hornet Special!
The Hornet Special has one major difference over every other car - you can customise its stats on the Car Select screen! Using the VR buttons and steering wheel, you can change the Engine, Steering and Suspension to better suit your playstyle, or just make an absolute monster of a car. For years it was assumed that this
car was an unfinished leftover of some kind, because people could only figure out how to access it via hacking - which bypassed the customisation aspect, and basically broke its stats, making it nigh impossible to actually use. It's speculated that the only people who actually
knew about the code to unlock the Hornet Special were superplay group Team Marubaku (MBK), who referred to it in their SuperPlay videos for the game but didn't share the code. In the end, over
20 years later, It was
The Cutting Room Floor who finally datamined the solution. Even the official Daytona 2 guidebooks don't mention this car!