Death Pulse

Target creature gets -4/-4 until end of turn.
Cycling {1}{B}{B} ({1}{B}{B}, Discard this card: Draw a card.)
When you cycle this card, you may have target creature get -1/-1 until end of turn.

The List

Onslaught

Target creature gets -4/-4 until end of turn.
Cycling o1o
Bo
B (o1o
Bo
B, Discard this card from your hand: Draw a card.)
When you cycle Death Pulse, you may have target creature get -1/-1 until end of turn.

The cycling ability and the triggered ability are separate. If the triggered ability doesn't resolve (because, for example, it has been countered, or all of its targets have become illegal), the cycling ability will still resolve, and you'll draw a card.

When you cycle this card, first the cycling ability goes on the stack, then the triggered ability goes on the stack on top of it. The triggered ability will resolve before you draw a card from the cycling ability.

You can cycle this card even if there are no legal targets for the triggered ability.