Was this character the only person in Batman: TAS to discover Batman's secret identity?

Question

In the Mask of the Phantasm film,

Andrea Beaumont discovers that Batman is Bruce Wayne when they catch Batman standing near his parents' grave.

Would this make them the first, possibly only, character in Batman: TAS to divine Batman's identity without Batman confiding in them?

Edit: Upon further consideration, excluding the What-If episode and dream sequences.

Answer 1

By no means. Across the DC Animated Universe, there are quite a number of people who have figured it out. Broken down by series:

Batman: The Animated Series and The New Batman Adventures

• Ra's al Ghul figured it out all on his own, as revealed in "The Demon's Quest". He possibly told Ubu, his manservant, but we can't be certain

  

• Talia al Ghul removes Batman's mask in her first episode; although she doesn't confirm that she recognized him, it's doubtful that she didn't. He's Bruce freaking Wayne

• Hugo Strange, who figured it out in "The Strange Secret of Bruce Wayne" by analyzing Bruce's subconscious thoughts

  

• Kyodai Ken and HARDAC, discussed in Nu'Daq's answer. Randa Duane, a side character in "Heart of Steel", learned at the same time as HARDAC

• Tim Drake, the second Robin (in DCAU continuity) broke into the Batcave in "Sins of the Father"

• It's likely that Zatanna figured it out. In her eponymous episode she connects Batman to "John Smith", the name Bruce used when training with her father Zatarra, but it's unknown at that time whether she connects him with Bruce Wayne. It's revealed in Justice League (and implied by an episode of The New Batman Adventures) that she did eventually learn that they were the same

As well, Bruce's old karate sensei Yoru probably knew, but this is never confirmed.

Superman: The Animated Series

• Clark Kent used his X-Ray vision to peek under the cowl in "World's Finest"
• Lois Lane learns later in "World's Finest" after, of all the stupid things, Batman's cape and cowl get caught in a printing machine and torn off

Justice League

• Presumably Hawkgirl, since she shows up uninvited in the Batcave in "Starcrossed"
• It's strongly implied in "Maid of Honor" that Wonder Woman figured it out. She and Bruce Wayne dance early in the first part of the episode, and she mentions the event to Batman at the end of the second part. Since Batman claims not to know what she's talking about, we can presume that he didn't tell her

Justice League Unlimited

• It's implied that Amanda Waller has figured it out in the episode "Ultimatum". That she knows will later be confirmed in Batman Beyond

Static Shock

The main character of the series, Static, figures it out when he meets Alfred in the Batcave, and then later sees him with Bruce Wayne

Batman Beyond

• Terry McGinnis, the main character of the series, figures it out when he stumbles upon the Batcave
• Joker is revealed to have learned from Tim Drake, after extensive torture

Answer 2

No- I'll have to do some digging to give you names and episode titles but from TAS I can point out at least three others- Ras Al' Ghul (actually had the balls to confront Bruce in the batcave), a ninja who fought both batman and Bruce Wayne and realized they were the same person because they had the same fighting technique, and the artificial intelligence HARDAC (or something like that) which learned Bruce's identity when batman interfered with its plans to replace all humans with android doubles. There may even be other examples I've overlooked.