The Porky Statue is an optional boss in New Pork City (Chapter 8) and is fought by examining it three times and answering yes on the third. It has 100,000,000 HP, but is easily defeated using the New Year's Eve Bomb item on it, as it reduces the enemy's HP to 1. It can also be defeated by using Lucas' PK Flash ability (although it may take a few tries).
The Porky Statue also plays a role in The Subspace Emissary. It chases Lucas down until Ness shows up after enough time has passed and destroys it, revealing Porky Minch, himself. It cannot be defeated when it chases down Lucas.
A guardian statue standing inside New Pork City that's clearly based on Porky himself. Investigate it, and the statue will turn hostile and start a battle. And it has 100,000,000 HP! It has very high stats, so you'll never win if you attack it straight-on. Thankfully, there's an item called "New Year's Eve" that can reduce its HP to 1--then you can defeat it with ease.
In Mother 3 and EarthBound, PK Flash has a variety of effects, including occasional instant death to the target. The Porky Statue has no defense against instant death, meaning that PK Flash can kill the statue without any additional help. This is presumably the reason why it works so well when Ness uses it in The Subspace Emissary.
The Porky Statue is supposed to resemble New York City's Statue of Liberty in its appearance. Instead of a tablet and a torch, the statue holds a comic book and a slingshot. Likewise, "New Pork City" is a play on the name "New York City".
The trophy description says that a New Year's Eve can defeat it, when it's actually a New Year's Eve Bomb.
Upon closer inspection, it appears that the comic book that the statue is holding opens from right to left instead of left to right. However, this is no mistake; with the EarthBound/Mother series being Japanese, the comic is most likely a manga, a Japanese comic that is read right to left due to the traditional Japanese style of reading.