The Axolotl is a powerful extra-dimensional creature whose power ranks massively above that of Time Baby, Bill Cipher, etc...  He is mentioned by Bill, while he was being erased by the Memory Gun during the events of Weirdmageddon.
It takes the form of a giant talking axolotl.
Alex Hirsch AMA
As Bill Cipher is being erased from reality, his final words are a distorted, reversed message which says: "A-X-O-L-O-T-L! My time has come to burn! I invoke the ancient power that I may return!"
On the portal aperture page, Bill writes a cryptogram which translates to: "ILL GET THIS PUPPY UP AND RUNNING ONE DAY AND NEITHER TIME BABY NOR THE BIG FRILLY KNOW IT ALL WILL STOP ME" (Axolotls have their gills on the outside of their heads, giving them a frilled appearance).
Throughout Bill's Ciphers section, there is code which says: "CURSE THE AXOLOTL EVERY CONSPIRACY IS TRUE."
In Journal 3 printed hard-copy (Gravity Falls merchandise) Stanford continues his part of the journal after having returned to Gravity Falls. In this he describes multiple dimensions in which he has traveled through including the axolotl's dimension. He describes the character as appearing as a female 'human' in the form that he saw.
In one of the invisible ink entries of the Special Edition of the book, Ford wonders if there is a polar opposite force to Bill in the universe, accompanied by a picture of a starry night that lights up in the shape of a constellation that resembles an axolotl in the black light.
According to Alex Hirsch, the book is non-canon to the actual series, as it follows a "choose your own adventure" format, having many different possible endings. However, he also said it does contain "one enormous 'canon' secret".
It is speculated that the canon secret could be Dipper and Mabel's encounter with the Axolotl in "the time and space between time and space." The Axolotl, a giant talking axolotl, lets each of them ask him a question. Dipper asks him "what [does he] know about Bill Cipher," to which he replies with this poem:
Sixty degrees that come in threes.
Watches from within birch trees.
Saw his own dimension burn.
Misses home and can't return.
Says he's happy. He's a liar.
Blame the arson for the fire.
If he wants to shirk the blame,
He'll have to invoke my name.
One way to absolve his crime.
A different form, a different time.
This suggests that when, before being erased from reality in the series finale, Bill gives a message that when reversed says "A-X-O-L-O-T-L! My time has come to burn! I invoke the ancient power that I may return!," he is actually invoking the Axolotl for redemption for his crime, and that there is one way to get absolved: he has to take "a different form" in "a different time." This would mean that Bill could return.
The line about "sixty degrees that come in threes" apparently refers to the fact that Bill's shape is an equilateral triangle: three sets of sixty degree angles (adding up to 180 degrees).
The line about "watches from within birch trees" may mean the illusion of eyes from the birch trees in the episode Dreamscaperers.
The Axolotl and Xolotl
A close relationship exists between the Axolotl and the Aztec God of Weirdness, Fire, Lightning, Sun (formerly), Death, Twins, Deformities and Sickness Xolotl-Nanautzin. It is speculated that these two are probably identical. In Myths it is said that Xolotl once turned into an axolotl for not being killed by his own twin brother, Quetzalcoatl. Unluckily, he was trapped in the sea he jumped and ended up forever being in this cage. But also Bill Cipher could be this god as well. Xolotl and Bill have many things in common: both want the apocalypse of weirdness, both have fire and lightning powers, both have something to do with twins, monsters, freaks, and both are defeated emperors. Also both made many deals with other people.
It can also be noted that in the "Gravity Falls: Journal 3," on The Oracle's page, we can see in the background an Axolotl. Just above said axolotl is a code that, when decoded, says "The opposite of Bill." (This could, however, refer to the Oracle - she is the physical and mental opposite of Bill, being sane, the opposite gender, having many eyes instead of one, and a benevolent figure.) This line strengthens the theory of an opposite/twins relationship between Bill (Xolotl) and The Axolotl.
TMS interview, July 2017
Alex Hirsch gave an interview with TheMarySue.com on July 14, 2017, in which he answered several questions about the series. When asked about the Axolotl, he said that while he considers the story finished, the Axolotl is basically a sequel hook in case he ever wants to revisit this world in the future (either an animated project or comics), though he stressed that he didn't actually have anything specific in mind at the moment - he just wanted to leave his options open:
- "In terms of Bill's secret message [about the Axolotl in the series finale]…I like stories that complete their emotional arcs, but still leave some lingering threads to chew on. It gives the fans something to theorize on, and it gives me a window back into that world if I ever choose to return to it."
- 220. "Weirdmageddon 3: Take Back The Falls" (mentioned)