No Burning Sun's Avatar's enter the battlefield ability will not resolve, so no damage will be dealt to the creatures.
In order for an ability to be put on the stack it requires legal targets. Burning Sun's Avatar ETB specifies (emphasis mine):
When Burning Sun's Avatar enters the battlefield, it deals 3 damage to target opponent and 3 damage to up to one target creature.
If you can not target one opponent and either one or zero creatures the ability will not go on the stack. This is covered in the comprehensive rules under here (putting the ability on the stack is the same as casting a spell, emphasis mine):
601.2.: To cast a spell is to take it from where it is (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. Casting a spell includes proposal of the spell (rules 601.2a–d) and determination and payment of costs (rules 601.2f–h). To cast a spell, a player follows the steps listed below, in order. A player must be legally allowed to cast the spell to begin this process (see rule 601.3), ignoring any effect that would prohibit that spell from being cast based on information determined during that spell’s proposal. (Such effects are considered during the check detailed in rule 601.2e.) If, at any point during the casting of a spell, a player is unable to comply with any of the steps listed below, the casting of the spell is illegal; the game returns to the moment before the casting of that spell was proposed (see rule 720, “Handling Illegal Actions”).
601.2c: The player announces his or her choice of an appropriate player, object, or zone for each target the spell requires. A spell may require some targets only if an alternative or additional cost (such as a buyback or kicker cost), or a particular mode, was chosen for it; otherwise, the spell is cast as though it did not require those targets. If the spell has a variable number of targets, the player announces how many targets he or she will choose before he or she announces those targets. In some cases, the number of targets will be defined by the spell’s text. Once the number of targets the spell has is determined, that number doesn’t change, even if the information used to determine the number of targets does. The same target can’t be chosen multiple times for any one instance of the word “target” on the spell. However, if the spell uses the word “target” in multiple places, the same object, player, or zone can be chosen once for each instance of the word “target” (as long as it fits the targeting criteria). If any effects say that an object or player must be chosen as a target, the player chooses targets so that he or she obeys the maximum possible number of such effects without violating any rules or effects that say that an object or player can’t be chosen as a target. The chosen players, objects, and/or zones each become a target of that spell. (Any abilities that trigger when those players, objects, and/or zones become the target of a spell trigger at this point; they’ll wait to be put on the stack until the spell has finished being cast.)
As an additional note, if your opponent gains Hexproof after
the ETB has been put on the stack, when the ability resolves it will still deal damage to what ever creatures have been targeted. This is covered on Burning Sun's Avatar gatherer rulings:
If the ability of Burning Sun’s Avatar has two targets and one becomes illegal, the other will still be dealt damage.