What happens if I play a card that has a tribute ability with the word target in it, my opponent chooses not to pay the tribute, and ability that applies has no valid targets.
Will the ability simply do nothing, can I not play the card because it will resolve illegally, or will my opponent be forced to pay the tribute?
The Tribute ability and abilities that trigger if the tribute wasn't paid are separate. It is perfectly legitimate for an opponent to not pay a tribute when there is no target for the ability that will trigger afterward. As with any such cases, that ability will then be countered automatically.
Why this is the case is not quite as straightforward, since the rules are a little roundabout about it, but tribute, being a static ability (like unleash) is just something that goes on as the creature enters the battlefield (what makes it feel very different is the delay introduced by the opponent choosing instead of you). The tribute-bound ability will trigger after that, when the creature is on the battlefield, and depending on the opponent's choice. At that point, if it has no target, it will fizzle normally (the same as when you control no other creature and cast Breaching Hippocamp).
Your tribute creature will enter the battlefield. Your opponent may refuse tribute, and the ability responding to no tribute can be auto-countered if it has no targets, but that will not make the creature itself get countered.
Will the ability simply do nothing, can I not play the card because it will resolve illegally, or will my opponent be forced to pay the tribute?
You appear to have a misunderstanding of the mechanism of spells being auto-countered when they have no targets, and how that extends to creatures.
Instants and sorceries get auto-countered if they have no valid targets for one reason: they (normally, or always AFAIK) place just one ability on the stack - a spell ability, which is the text on the card. If that spell ability gets auto-countered, the entire card might have no effect, because it's all the card did.
However, creatures aren't a card that just have one single effect. When you're summoning a creature with tribute, you will do all of these things separately and independently:
#1 or #3 can be countered independently. If someone plays Essence Scatter on your Nessian Wilds Ravager, the entire creature card will go to your graveyard and #2 and #3 won't happen.
However, if #3 gets countered (including by #3 having no legal targets), the creature is still going to enter the battlefield - it's already done so - and countering the individual ability has nothing to do with countering the card as a whole.
