The X and Y buttons are the ATTACK. The A and B buttons are JUMP. Pushing A+X or Y+B will result in a magic attack. Do NOT do that, do not use magic. As long you just jump and attack, you'll be fine. The first level is pretty simple.
Slash the enemies as they come and watch out for them overhead on staircases if you choose to walk under them. You don't want them to drop off on top of your head or walk down the staircase and have their feet run into your face. Yes, it's one of those impossible 2D retro gaming paradoxes when a person walking past a staircase on ground level can be hit in the face by someone's feet walking down a staircase above and behind them just because they are lined up. What retro gamer doesn't take humor in that? If you do take the stairs, take care not to hop of onto or into an enemy as well. Another tip is the bipedal bears (yes, really) will throw what looks like Guile's Sonic Boom (i'm not joking). Be sure to duck to avoid those, but don't walk toward them crouching either as they will notice and duck to hit you, too.
Once you get to the first boss, the chimera, you need to time it's jumps to run under him and avoid being jumped on. When he lands, spam the attack button and occasionaly turn to hit other baddies. If you free the ally from the lower door earlier in the level (the Amazonian woman, you will need a key from a chest or swallowed by an enemy to free her) she has a long range of attack with her spear and will help you greatly in the chimera boss battle.
Just keep trying. The level is very short and simple, so if you're messing up, the prompt will tell you that you failed the "Ninja Skills Achievement" in red text, so pause and restart. I took me about 10-15 tries, so hang in there. It's definitely possible.