I think I can help you beat the liz easier. After u attack the bio, he will start to chase you. I recomend you run really fast in the other direction, and jump if you think the pool is there. If you run too fast, bio will chase you with his tail and slam you with it. If he chases you with the tail, jump, turn around, and homing attack for a small boost. When he uses the hyper energy attack, keep rings in sight, and run away. Try and move as far away from those as possible. That's the bestway to dodge those. When bio does the forcefield attack, jump, homing attack the lowest dot, wait until it makes you go really high, then rinse, lather, and repeat. If you lose rings, abandon your attempt IMMEDIATLY When he finally lifts you in the air for the last attack, my advice is simple: Cross your fingers, and randomly move the control stick (if u can do both at the same time) The liz took me 3 tries to beat when I met him in story. I beat him using this strategy, so try it.
Edit: oh, you meant mech as in the tail's/eggman fight..... Just hit the center pillar when your opponent is near it, and it will take a chunk of their health away, and stun them. When they're stunned, use your lazer+your gun.