Sylas vs Jax

Weave an auto after each spell: Petricite Burst (passive) turns it into a chain swing around you, with bonus magic damage.

Save Kingslayer (W) to finish or to save yourself when your health drops: its healing grows with your missing health.

To engage, cast Abscond (E), then recast within 3.5 seconds: Abduct (E) pulls you to the first enemy hit and knocks them into the air.

Cast Hijack (R) on the enemy whose ult can turn a teamfight: you keep a copy of it, cast with your own stats.

Take a short trade, then back off: Relentless Assault (passive) increases his attack speed with each consecutive auto.

During Counter Strike (E), back off instead of attacking: he dodges your autos, then stuns nearby enemies, dealing more damage per dodged auto.

Trade right after Counter Strike (E): it's both his defense and his only stun, and it has a 17 to 9 second cooldown.

In the late game, don't leave his split push unanswered: send someone to hold his lane, or force an objective on the other side of the map.