Please make sure to wake me up at 6 AM tomorrow.

Literal

Tomorrow morning 6-o'clock [at-に] forget-without wake-up please.

忘れずに ('without forgetting') uses the classical negative ~ず + に as an adverbial modifier. Two に particles appear: temporal (6時に) and the adverbial ずに. The transitive 起こす ('wake someone') with its object omitted.