Evelynn has very low early jungle power, so avoid engagements with strong early junglers like Lee Sin or Xin Zhao and focus on farming.
Maintain a safe jungle path until level 6, and make plays by creating variables with surprise ganks using stealth.
Even her untargetability and magic resist reduction abilities don't fully compensate for her early weakness, so play carefully to aim for the late game.
Avoid fighting Rengar nearby brushes. His empowered Battle Roar (W) can cleanse the charm on Allure [W], so avoid fighting him altogether. Focus early game on jungling instead!