Solidarity of Heroes can target any creatures, not just ones with +1/+1 counters on them. Notably, heroic abilities of any target creatures that put +1/+1 counters on that creature will resolve before Solidarity of Heroes.

If all of the spell's targets are illegal when the spell tries to resolve, it won't resolve and none of its effects will happen. If one or more of its targets are legal when it tries to resolve, the spell will resolve and affect only those legal targets. It will have no effect on any illegal targets.

You choose how many targets each spell with a strive ability has and what those targets are as you cast it. It's legal to cast such a spell with no targets, although this is rarely a good idea. You can't choose the same target more than once for a single strive spell.

If a spell or ability allows you to cast a strive spell without paying its mana cost, you must pay the additional costs for any targets beyond the first.

If such a spell is copied, and the effect that copies the spell allows a player to choose new targets for the copy, the number of targets can't be changed. The player may change any number of the targets, including all of them or none of them. If, for one of the targets, the player can't choose a new legal target, then it remains unchanged (even if the current target is illegal).

The mana cost and mana value of strive spells don't change no matter how many targets they have. Strive abilities affect only what you pay.