Agatha of the Vile Cauldron's first ability affects only abilities of creatures you control on the battlefield. The costs of activated abilities of creature cards that work in other zones (such as cycling) won't be reduced.

Activated abilities contain a colon. They're generally written "[Cost]: [Effect]." Some keyword abilities are activated abilities and will have colons in their reminder text. Triggered abilities (starting with "when," "whenever," or "at") are unaffected by the cost reduction ability of Agatha of the Vile Cauldron.