Gorgon

You can recruit a Gorgon at the training grounds. They are as likely to appear as a Queen and cost just as much, so you've got to be lucky AND wealthy, but you can get a Gorgon.

They can be overpowered if they can lock enough of your pieces at once, but often you can plan against it either by killing the Gorgon early (the AI almost always puts it in the front row) or planning some counterplay against it. Pinning a gorgon to the enemy King is brutal if you can manage it.

Immortal

I'd have to agree they are rather annoying. Unless you're specifically using a strategy where you take most pieces with your king (presumably, you got a prince and, ideally, the relic that gives gold when your king kills enemies), you're not going to be prepared to fight a piece that can only be taken by the king, especially if the enemy king insists on standing next to it.

Could they just make the starting relic that Insta-kills lone kings ignore immortals?

Personally, I'd add Pegasus Rider to the list of "not overpowered but really annoying" pieces as their movement pattern is hard to keep track of, but of course, the AI always uses it perfectly to check your king or take your favorite piece from across the board.

Princess

If you're only looking at the piece itself, then I'd agree. However, this ignores the Princess's best trait - the AI is downright terrified of letting a Princess promote. Having a Princess defend one of your pieces will stop the AI from capturing that piece (unless it can immediately capture the resulting queen). Have her defend a Prince, a Pawn, or each other if you've got more than one.

(And having multiple copies of a slow-moving piece hard counters a certain witch)

One of my least favorite fights is against an AI that has the princess artifact. Especially if they have more than one Princess.

Speaking of the Pawn, they are useful for the opposite reason of the Princess - the AI is so unfazed by Pawns that marching one into promotion with little or no resistance is fairly common.

Mirror Queen

This piece is mostly underpowered for what it takes to get one. If she can capture your enemy's strongest piece (downright epic if she nabs a witch!) awesome. But you don't often get a clean shot at the enemy's strongest piece, and you have to be sure not to take anything else lest she transform into that instead.

Catapult, Blade Dancer, Infiltrator and Reaper

Well, the fight against Tabitha is something you'll need to take into account when building your team. If you've got all four of these on your team, then Tabitha is going to be terrifying. You might want to plan out not having too diverse a set of movements before Tabitha or consider sacrificing your pieces against hers (she can't copy a dead piece's movement).

Musketeer

I hate this gun. Basically, it's a free piece on turn 1, and there's nothing you can do about it unless you're lucky enough to have an immortal across from him (which you have no way of knowing or planning). Even later into the battle, just the ability to capture without moving without needing an item or an artifact is seriously OP.

Spiked Shield

Yeah, I'd have to agree it's underpriced for what it does. It's not game-breaking, but it really should be priced higher.

Swap Relic

Yeah, the game lets you (or the AI) swap pieces with impunity if you have this relic. I'm not sure why they let you swap any two pieces; it really should've required they be next to each other.

Fire Gem

I can only assume this was added to the game before the Prince was, and then the item was never revisited after. An item that protects 1 unit from 3 enemies in the entire game? Worth 900+ gold? Really?

It's been a while since I've played this, thought I'd share what I remember about these pieces.

- Gorgon
I agree, it's a total nightmare. The best way to deal with this piece is to have a knight-like piece that can jump over other pieces and attack them. Or kill them immediately with Reaper or some other power up (chain them and end them). Gorgon heavily punishes clumped up armies that stick to each other for defense.

- Immortal
Used to be A LOT more annoying when it could put your King in check and couldn't be taken by them either. However, I find that it's a lot more annoying for the AI to deal with than the player. The Mounted King does a great job of defending your pieces against the Immortal while also attacking them. You can avoid draws by forcing the enemy king away from the defense of the immortal, then take it with your king.

- Princess
I don't think it's under powered, just balanced. As toad said, the AI is terrified of this piece and you can abuse the AI with it. You can also use the rock breaking relic which counts as a kill for the Princess to turn it into a Queen. Aside from that, the Princess is very mobile diagonally which can them to support other pieces quickly.

- Mirror Queen
I don't think it's bad. It's good for trading off pieces and not having the risk of losing your queen permanently like with the Glass Queen.

- Tabitha
You should immediately trade off your strong pieces when fighting Tabitha so she becomes much weaker as the game goes on.

- Musketeer
100% agree, it's OP and extremely hard to take care of. The AI can start with the Musketeer directly facing your pieces and can very easily skewer/pin your army. The best counter to Musketeer are rocks and the Immortal to act like shields. Spiked shield also kills it. Prince can also allow the King to act like a shield.

- Fire Gem
It's not under powered and very much worth the price. It trivializes every boss fight. Yes, the Prince is pretty OP too, but the gem is great as insurance in case you blunder and lose the Prince somehow.

2 phoenix's is basically an instant win, lol. just run them up the board, and sack one after the other, after the other... helps to have a prince. effectively no way to really lose imo