Amumu vs Lillia

Save a charge of Bandage Toss (Q) after your engage: the spell has two, and the second catches an enemy who escapes with a dash or Flash.

Wait until several enemies are in range to cast Curse of the Sad Mummy (R): it stuns every enemy around you and curses them.

Keep Despair (W) on against tanks: every second, it deals a percentage of their max health to nearby enemies.

Full clear with Despair (W) and Tantrum (E), then gank: both hit every nearby monster, and Tantrum's cooldown drops when you get hit.

Against Blooming Blows (Q), stick to her or back out of range: only the outer edge of the zone adds true damage.

Get out of the center of Watch Out! Eep! (W): the zone deals much more damage there than at the edge.

Dodge her spells, even Swirlseed (E), which rolls to the first enemy: each one marks you for Lilting Lullaby (R), which puts every marked enemy to sleep.

If you have CC, use it on her: with no dash, she relies on the move speed Blooming Blows (Q) gives her for each spell that hits.