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 after the player has finished the sewer area in New Pork City. 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, although the success rate is very low. Upon defeat, a man nearby will give Lucas and company the "Trivia Card 4" item.
The Porky Statue also plays a role in The Subspace Emissary. It chases Lucas in The Ruined Zoo 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.
A statue of Porky that Porky ordered built to honor the great exploits of Porky as acknowledged by Porky. It depicts Porky in his carefree childhood days in Onett, a comic book in one hand and a slingshot in the other. Be warned—this statue is also an incredibly tough enemy!
In Mother 3 and EarthBound, PK Flash has a variety of effects, including rare instant "death" to one, or even all targets. The Porky Statue has no defense against the OHKO properties of PK Flash (however, it is immune to all other effects of PK Flash), meaning that PK Flash can destroy 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.