Maintain spacing to dodge (Q) poke and respect Malphite's passive shield windows to reduce damage taken.
Power spikes
At level 6, use (R) for high mobility and burst to execute all-ins or escape (R) engage; track his ultimate cooldown closely.
After completing first AP burst item, increase wave pressure and trade confidence to punish Malphite's low early poke damage.
Respect Malphite's level 6 (R) engage and his first armor item spike which reduces your physical trades but is less effective against your magic damage.
Win conditions
Use (R) mobility and burst to pick off Malphite before he can stack armor and reach teamfight power.
Pressure waves and punish cooldowns to deny Malphite a calm scaling lane and force him into defensive play.
Transition into teamfight disruption and flank pressure leveraging your mobility and burst to capitalize on Malphite's predictable engage.
Tip: For Aurora vs Malphite, read overview, trading pattern, and danger windows first for a fast Top lane check.