Couldn't figure out how to beat the second boss (even after accidentally doing the secret input), and my next few attempts didn't even make it to the boss, so I threw in the towel. Cool game, very gorgeous graphics, but the feel of the platforming wasn't really to my taste, so going through the spikes of that level a fourth time didn't sound appealing. My skill issue aside, I recommend this game.
The trick to beating it easily for me is to just stand right up against the shield (the shield doesn't do contact damage) and then when it goes to swing, jump and hit it in the head. It kinda seems like you will get hit but if you time it right it will miss. Also one small tip for anyone struggling with the platforming, the game really wants you to just kinda hold forward and keep going, instead of trying to stop on a small platform, just jump as soon as you land on it instead and you won't have to deal with sliding.