You must choose two targets as you cast Feral Contest: a creature you control and any other creature. If you can't (because there's only one creature on the battlefield, perhaps), then you can't cast the spell. Note that the second target may also be a creature you control.

If just the first targeted creature is an illegal target by the time Feral Contest resolves, it won't get a +1/+1 counter. However, the second targeted creature is still affected by the blocking restriction the spell imposes, so it'll have to block the first targeted creature that turn if able.

If just the second targeted creature is an illegal target by the time Feral Contest resolves, the first targeted creature will get a +1/+1 counter, but the second targeted creature won't have to block it that turn.

Casting Feral Contest doesn't force you to attack with the first targeted creature that turn. If that creature doesn't attack, the second targeted creature is free to block whichever creature its controller chooses, or block no creatures at all.

If you attack with the first targeted creature but the second targeted creature isn't able to block it (for example, because the first targeted creature has flying and the second one doesn't), the requirement to block does nothing. The second targeted creature is free to block whichever creature its controller chooses, or block no creatures at all.

Tapped creatures, creatures that can't block as the result of an effect, creatures with unpaid costs to block (such as those from War Cadence), and creatures that aren't controlled by the defending player are exempt from effects that would require them to block. Such creatures can be targeted by Feral Contest, but the requirement to block does nothing.