Toxrill. the Corrosive's second and third abilities apply to all creatures you don't control with slime counters, even if those slime counters came from a source other than Toxrill's first ability.

Another card, Sludge Monster, causes non-Horror creatures with slime counters on them to lose all abilities and have base power and toughness 2/2. If you control both Toxrill and Sludge Monster, those non-Horror creatures are 2/2 creatures with no abilities that also get -1/-1 for each slime counter.

Toxrill's third ability triggers when a creature an opponent controls with a slime counter on it dies for any reason, not just due to its toughness being decreased by Toxrill's second ability.