Amalthea was the goat that fed Zeus when Rhea wanted to protect him from Cronus, hiding him in a cave in Crete. Other versions say that she was actually a nymph, who was in charge of feeding him with goat's milk. But in some parts I have found enigmatic references that say that Amalthea was a "terrifying" animal, and that even the Titans and the gods feared her. I have tried to go deeper into this aspect, but perhaps I have not known how to search well, since I have not found anything. Where does it come from that Amalthea was so terrible? I know that with Amalthea's skin, Zeus later made his shield, the aegis, which he later gave to his daughter Athena. Was Amalthea not a normal goat? Was she more of a monster than a goat, perhaps?
Regarding Different Versions of Goat-Stuff
There is a great variety of traditions surrounding the birth and rearing of Zeus, and among these, as you have already observed, there are different renditions involving a she-goat or a similarly named creature. From what I have found, these renditions can be broken down into three main categories of versions. The commonest of them is the one in which Amalthea is a she-goat that suckles the baby Zeus.
You have also noted the second most common version, in which Zeus is still suckled by a she-goat, but Amalthea is the name, not of the goat, but rather of a young woman, or a nymph of some sort, who has a she-goat as a pet, or as a head of livestock, from which she obtains milk to feed the baby god.
In the third version Amalthea seems to get replaced by an altogether different sort of creature who has a "goat-like" name, i.e. containing the root word aig- or aix, generally understood as simply meaning "goat." From all accounts the nanny-goat in the other two versions seems to be an ordinary mortal garden-variety bovid, nothing scary or monstrous at all about her.
Two ancient writers, however, tell a couple of stories about a different order of entity who seems to be the equivalent of Zeus' nanny-goat, but deviating quite dramatically from the animal who supplies him with milk in his infancy.
The Aigis Monster
In Book 3 of the Library of History, Diodorus Siculus provides a fairly unique version of the story of the Titans' War, in which (in Ch. 68) Amaltheia is "a maiden of unusual beauty" with whom the Libyan king Ammon (= the African form of Zeus) has an extramarital affair "near the Keraunian Mountains". The name of the mountains would appear to be a reference to the Greek word for "horn(s)," i.e. like those of the goat Amalthea from the commonest version of her story. This maiden Amalthea then bears Ammon a son named Dionysos [Dionysus], who grows up to fight a war against the Titans.
Further on in Ch. 70, Athena, who here is also a Libyan goddess, has grown up in the region, training in various skills and being "cultivated... in the arts of war". Gaia, the Earth, had given birth to "a certain frightful monster" named Aigis [Aegis], which "breathed forth terrible flames of fire from its mouth". Emerging first in Phrygia, the monster burned a path of destruction throughout the entire region, across the Taurus Mountains and all the way to India, turning back around to scorch a swath of flames via Mt Lebanon, through Egypt and on into Libya itself.
Athena, with the use of intelligence, courage and bodily strength, slays the beast and then wears its hide. For this reason Gaia sends the Giants to fight against the gods "but they were destroyed at a later time by Zeus, Athena and Dionysos," together with the other deities. The idea seems to be that the Aigis worn by Athena simply received its name directly from the monster whose skin it was.
Finally, though, the version that you seem to be referring to does not seem to have any character actually named Amalthea in it, although it appears in a passage from the Roman writer Hyginus in which he is narrating different myths explaining the origins of the "goat-signs" in the constellations Auriga and Capra, which include the tales of the nanny-goat/ nymph-princess Amalthea.
Having gone through three different renditions of that mainstream myth in Poetica Astronomica 2.13, he goes on to mention a daughter of Helios (the Sun), whose name was Aix [Aex]. She, he says, had an exceedingly beautiful body, "but in contrast to this beauty, had a most horrible face. Terrified by it, the Titans begged Terra [= Gaia] to hide her," to which the earth-goddess acquiesced by concealing Aix "in a cave in the island of Crete", where she later became Zeus's nurse.
The narration then jumps to an oracle in which Zeus, on his way to war against the Titans, is told that in order to win he has to protect himself "with the skin of a goat and the head of the Gorgon" and that the Greeks call this the aegis. The hints are more implicit than spelled out by the storyteller but presumably the idea is that Aix is the Gorgon in question and that she was some sort of goat-like creature.
Maybe she was a gorgeous woman with the head of a monster goat(?)... More enigmatically, we are not told whether Zeus kills her in order to wear her skin or if she has already died previous to the war, or such. At any rate, Zeus follows the oracle's instructions and thus wins the war.
Covering the remaining bones of the goat with a skin, he gave life to them and memorialised them, picturing them with stars. Afterwards he gave to Minerva [Athena] the aegis with which he had been protected when he won.
Hyginus's Aix/Aex, from my understanding, is the equivalent of Diodorus Siculus's Aigis monster. According to Theoi.com's interpretation of Aix:
Like the aigis-shield itself, she symbolised the storm-cloud. Her name means both "Terrible Goat" and "Fierce Storm" for the Greek word aigis contains the double-meaning of "stormy" and "goatish"...
The Gorgo Aix, was also described as the nurse of Zeus, and in this case she was a monstrous counterpart of the goat Amaltheia.
Based on the narratives, the nanny-goat Amalthea herself is a positively benign animal, symbolising a source of nourishment and plenty, since one of her horns, upon breaking off, is supposed to produce whichever food or drink that its bearer desires.
The stories featuring the monster Aigis, and the Sun's daughter Aix, are essentially alternate versions in which no goat character remains, and the only one featuring a creature literally named "Goat," of whom the Titans are terrified, is Hyginus's yarn in which a daughter of the Sun is not an animal but a sort of horrifically beautiful "Gorgon."
Without citing any particular references, it will be hard to know quite what is meant. There isn't anything particular concerning this in Theoi (a fairly comprehensive collation of primary sources) or Wikipedia, so it could be anything from pure fabrication to a misunderstanding to a rare or late tradition.
That said, the only thing I could think of that relates to Amalthea and being terrifying is the use of her hide in crafting the aegis, which as you can see below, when combined with the head of Aex the Gorgon, provided him a protective shield in the war of the Titans.
Pseudo-Hyginus, Astronomica 2. 13 (trans. Grant) (Roman mythographer C2nd A.D.):
"But when Jupiter [Zeus], confident in his youth, was preparing for war against the Titanes, oracular reply was given to him that if he wished to win, he should carry on the war protected with the skin of a goat, aigos, and the head of the Gorgon. The Greeks call this the aegis. When this was done, as we have shown above, Jupiter, overcoming the Titanes, gained possession of the kingdom . . . Afterwards he gave to Minerva [Athena] the aegis with which he had been protected."
So, before Zeus gave it to Athena, he used it to fight the Titans. This is likely the origin of the confusion about her being terrifying.