The game is quite good. But you should know that another author has ripped off your game, replacing the main character with their own rip-off character and then claiming it as their own. Since I did not see mentions that the edit was authorized, I thought you should know. (The game is 'Hopy Go Go')
Regarding the game itself, the game is a passable improvement over the original. Although I did like the greater enemy variety, new levels, and most importantly, the new bosses, the game suffered from a rather glaring issue: it is painfully short.
This is really a shame as the improved controls, faster speed, and improved secrets (I especially liked the inclusion of Donkey Kong Country-styled bonus levels) really do much for the game's longevity. I think the biggest problem is quite simple: the difficulty does not climb nearly as fast or enough, which only serve to highlight how short the game is. Likewise, getting the Dragon Coins and all the Blue Gems only give you upgrades, which feels like a waste when the game is perfectly beatable and balanced with the player never using upgrades.
I suggest you take a further note from Donkey Kong Country... and even maybe from Kirby.
In the old-school Kirby games, if you rush to the end and do not take the time to properly complete the game, the villain's back-up plan cause your adventure to end in failure anyway (the villain take over the world despite your efforts). The consequence for failing to properly completing the game need not to be that harsh but I think that having access to secret levels or even maybe a bonus ending for those who go all the way might help make finding everything feel more rewarding.
Regarding the difficulty, I think you shouldn't be afraid to crank it up. I do not mean to turn the next game into one of those 'die a bajillion times per room' platformer but rather, look at the Mario serie or other such platformers ; have the difficulty begin and stay relatively low but have it climb over the course of the game.
This is pretty important because the difficulty spike in this second game is truly horrid ; since the difficulty climbs so slowly and the game is so short, the difficulty spike when you reach the bosses is unreasonable. You go from extremely easy platforming stages to shockingly unforgiving bosses who aggressively hug you for collision damage while filling the screen with projectiles. This isn't a problem ; they're nowhere near excessively brutal. But it feels jarring because the game is so short and easy. It would feel better if you had more levels and a harsher difficulty progression to really 'telegraph' the bosses (unless your intent is to concentrate the difficulty into the bosses, in which case you need more of them).
I must address the final boss in particular. Dark Wizard's first form is a fantastically designed boss fight and I must commend for it. The only thing it really lack is extra attacks or an 'angered mode' when at low health. How well-designed this fight is only serve to highlight how badly designed the proper final fight is.
Dark Wizard's final form is very disappointing. It is full of what one may call 'fake difficulty' ; Dark Wizard's attacks are not even threatening. The problem is that he spend almost all of the fight being invincible (a mechanic exclusive to that form) and his attacks abuse the fact that you can't duck with frustrating effectiveness. It does not help that this boss's two attacks make for a very repetitive fight, especially since unlike other bosses, this form is not especially mobile.
Regarding the setting, I feel that it is pretty nice except for one glaring issue: the bosses are not especially expressive or interesting. While Drake and the normal enemies are suitably cartoony and full of personality, the giant skeleton and Dark Wizard are surprisingly bland and boring.
Frankly, I feel that the bosses should be unique designs, with suitable expression and personality. It would help make the boss encounters much more unique. This is especially true for Dark Wizard, who is an especially boring antagonist. Which is a shame ; I feel that it would be fitting for Drake to have a suitable foil/opposite. Maybe Dark Wizard could try creating his own twisted version of Drake only for it to backfire, resulting in a dark dragon who he can't control? And that, although disliking Dark Wizard as much as Drake, ends up thinking that using dragon powers just to keep the peace if a waste of an opportunity...
Just an idea.
To summarize. The game is great but suffer from short length and a lackluster final boss. Difficulty balance issues are there but are not crippling (stages too easy causing bosses to feel too overwhelming).
My suggestions is to add more rewards for finding secrets (extra levels, extra ending). Boss design could be improved, especially considering main character and enemies design.
Don't know if you'll end up reading this but if you do, I hope it will help.