Stepper motors can't accelerate instantly to full speed or anything like it, you need to ramp-up the step-rate or you lose lock and they mis-step and stall (that screeching noise). The AccelStepper library is the first requirement - and eventually to go faster you have to overcome back-EMF which means a chopper-drive IC and a higher voltage power supply - gets more complex then.
Also mechanical resonances can cause lose-of-lock too - mechanical damping can help but micro-stepping is a really good at combating the severity of resonance.