The opening scenes. Most would panic at the sight of alien monsters, even if their kids were being kidnapped. Jade grabs a flaming stick and starts handing out beatings like free candy.
The music certainly makes it more awesome, especially when the game goes into slow motion for a more operatic section of the track.
The battles with the Teratosaurus on the hovercraft. Partly it's the build-up with the alarm around the city, partly it's the music, partly it's the sheer size of the monster - and how satisfying it is to start cutting it down segment by segment - and partly it's just how chaotic the battle can get when you're pursuing the beast.
The battle with the penultimate boss of the game, General Kehck. You pilot an old ship made from junk and with only two functional weapons. He's riding a huge, black, flying Spider Tank which is between three and four times larger than your vessel and shoots Frickin' Laser Beams to the point of Beam Spam and missiles bigger than your whole ship. You're being pulled by its tractor beam, and you're battling through a canyon in the moon. And the guy's an incredibleLarge Ham, even for this game. Of course, the music it plays helps matters also.
The Roofhopping section near the end of the game (with Jade getting personally chased by General Kechk) is Beyond Good And Evil at its most awesomely cinematic.
Jade is awesome in herself if you think about it. Unlike other game heroes who have a Hyperspace Arsenal of endless weapons, Plot Coupon and convenient power-up, Jade gets by from start to finish on a camera, a Jo Staff and one range weapon with no upgrades or New Powers as the Plot Demands(Pey'j's unexpected recovery and end cutscenes notwithstanding of course). You fight the Final Boss, the Elite Mook and basic mooks with the same abilities, using Jade's human skills of timing, will and wits. This makes her ten times more awesome than Mario, Link or Gordon Freeman.