Can I respond to the mana payment for Oppressive Rays?
No, you have no opportunity to tap your opponent's creature after they have decided to pay the {3} to attack, but before they are already tapped and attacking.
The choice to pay mana is done as part of the declare attacker steps; they actually tap their own creature as part of attacking with it right before they pay the {3}, and you don't get priority to do anything until after they have finished declaring all attackers.
From the rules:




Declare Attackers Step





508.1. First, the active player declares attackers. This turn-based action doesn’t use the stack. To declare attackers, the active player follows the steps below, in order.



508.1a The active player chooses which creatures that they control, if any, will attack.
508.1f The active player taps the chosen creatures. Tapping a creature when it’s declared as an attacker isn’t a cost; attacking simply causes creatures to become tapped.
508.1h If any of the chosen creatures require paying costs to attack, or if any optional costs to attack were chosen, the active player determines the total cost to attack. Costs may include paying mana, tapping permanents, sacrificing permanents, discarding cards, and so on.
508.1i If any of the costs require mana, the active player then has a chance to activate mana abilities (see rule 605, “Mana Abilities”).
508.1j Once the player has enough mana in their mana pool, they pay all costs in any order. Partial payments are not allowed.



508.2. Second, the active player gets priority.



You of course could tap their creature during the start of combat step, but you won't know whether or not they plan to pay the {3}, and if you choose to do so then they won't waste their {3} to allow it to attack. But once they declare it as an attacker, and you get to cast Dizzying Swoop, it will already be tapped and Dizzying Swoop would have no affect on it (though it would still be a legal target; it would be generally pointless).