One thing I've been fascinated to see in Pathfinder is how it forces you into having certain characters in the group.
Okay, so was this the real reason for the post?
Considering how generic the first question was, but then your response to answers being regarding a specific situation, it feels a little like you are aiming to soapbox, rather than seek any real help.
If that's not the case, and your post was simply a reaction to the situation, then I apologize. It just felt.. "hinky".. how the thread progressed.
If you don't have the first three, you will NOT be able to deal with the threats in a typical adventure.
"Typical" adventure? That monster of a boss is anything but typical.. You can't build it according to the normal rules for Animated Objects (between fire damage, fast healing, etc).
Besides, the rules for animated objects involved Hardness in 3.5e as well.. this is hardly a Pathfinder thing. Is it upsetting that they didn't take it out? Maybe... but this is literally the first time I've seen an Animated Object with Adamantine hardness, so it's quite a rare situation.
Regarding that specific encounter, it's up the DM to adjudicate if energy damage would affect a
specific creature/object. Considering it's "super heated" metal, I'd be inclined to allow Cold damage to at least do full damage, if even bypass hardness, simply because the rapid cooling will cause stress on the metal. Voila, fully within core DM adjudication to allow a Cone of Cold to give this thing a bad day.
What 3e D&D (3.0, 3.5 & Pathfinder) does is emphasize how bad it is to
specialize. If you have a lot of options available (casters having scrolls and wands, fighters having alternative weapons and combat styles, etc), then you can be ready for a wider variety of encounters.
But it's rare that you run into something that needs "Macguffin X" to win, and nothing else works, so your pooched if you don't have it.
Lastly, I'd suggest putting up spoilers for any discussion on the encounter or adventure for the creature, because this went from a general "How do you beat hardness" to "How can I kill this specific creature in a printed encounter".
People might be wanting to play the game you are posting detailed information about without warning.