@Michael5927 One thing new hosts are often surprised to learn is that the so-called "deposit" is fake. Airbnb does not charge or hold any amount you specify, and it has no bearing on whether a damage claim will be resolved in your favor. Nothing wrong with putting some random number there as a deterrent, but don't operate under the assumption that it's going to be there if you need it.
You can request reimbursement for physical damage when necessary, but you will have to accept that a negative review is a likely consequence, so it has to be worth it. In this case, a noise complaint has no tangible monetary value and the dog hair is a normal result of allowing animals (including service animals, which Airbnb requires you to accept), so Airbnb would not back you up on a claim for those. That leaves the broken bed, which is seldom ever the result of an individual guest abusing the furniture. After all, sleeping on a broken bed is much more of an inconvenience to the guest than repairing it is to the host. This doesn't add up to a good case for reimbursement.
I'm not even sure I'd call this one a "bad tenant," though it really depends on the nature of the HOA complaints and how the guest responded if/when you addressed it. Accidental minor damage and hair from a permitted animal are common things you'll encounter with this kind of rental, certainly nowhere near the horror stories you'll see every day when perusing this forum.