Firstly can say that game runs with default settings just fine and no menu flickering at all (it runs fine with any settings if you choose "SSE4 + any Hardware renderer" as base), but if you want to run game in 120fps you can adjust your settings like in
that video (but I recommend to set Interlacing to Auto if you see dithering picture).
There is a bug if you adjust FPS limit to 120fps: after game's main menu appears you will hear that music degrade and start to scream, then your game will stuck after you try to load game (or start new game). You can try to relaunch pcsx2 and launch the game using "Boot ISO (full)" button + don't use Turbo mode until you successfully load your savegame. But that advice is not always work and I still can't understand how to reproduce that bug - it appears sometimes and in different conditions. Sometimes music don't degrade to screaming noise, but music always stutters in main menu if your game is in 120fps.
I am not sure, but if your game is launched in 100fps (not 120) you will never encounter that bug (about game stuck after loading savegame), so you can start the game successfully in this case, but the music in main menu will always stutter as it was in 120fps mode.
Mentioned bug never appears if you launch the game in 60fps and music plays with no defects.
For those, who faced "no HUD / no main menu" problem, I can say that I had this problem on the Russian NTSC version. The cause of that bug was game's multiloader (it is menu with language selection that launches right after you open the game). To fix the problem I just applied patch that deletes all language except one and thus deletes multiloader. It is named SLUS-21372_ER-E if you would like to keep only English language, SLUS-21372_ER-R if you want only Russian, SLUS-21372_E-ER if you want to revert the changes back. After applying the patch my game runs with HUD even if I choose default settings.
Here is the patches:
SLUS-21372 The Legend Of Spyro A New Beginning Rus-DeRus patches.zip (Size: 607,9 KB / Downloads: 555)
Game CRC: 0xD03D4C77
Emulator version: pcsx2-v1.5.0-dev-2234
BIOS Used: USA v02.30 (20/02/2008) Console
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PC specs:
Intel i7 4770K
NVIDIA gtx760
Windows 10 x64