maybe this will help

I pondered this very point for at least a year after seeing this movie, but then a thought dawned on me that set my mind at ease and I haven't thought about it since: Batman was relying on Robin's learned skills to buy time--first, he saved the victim who had no chance whatsoever of saving herself; second, he saved his apprentice/sidekick who he hoped would find a way to slow or stop his fall, adding much-needed seconds. Luckily, it worked. It was the only logical decision, and he came to it much faster than I did--he's a smart man.

Dropping order

Robin is dropped before Chase and so Shase is nearer to Batman when he comes to the rescue, therefore so as not to waste time Batman saves them in the order he reaches them.

Here's what I think...

I thought about this but then I realised the following. The Riddler's base is on an island and one tiny little hollowed out telescopic rusty shaft is capable of supporting the rest of the base with that huge throne room and massive 'box' on it. This serves no purpose other thanto provide a great height from which characters can fall. The Throne room itself is filled with swirling bright neon question marks which serve no purpose other than to look pretty. The whole final twenty minutes or so of this film are the most absurd campy fantasy scenes I think I've ever seen in a major studio blockbuster. Therefore I surmise that: There was no real logic to Batman's actions during this scene. Genghis Schumacher & his Avenging Hordes of Camp simply wanted to do a big special effects type stunt to give the audience something nice to look at.