Most of what you describe comes from The Book of Three, the first book in the series.
The protagonist is Taran, an orphan.
His master is Dallben the Enchanter, a fairly standard wizard type:
Dallben, master of Caer Dallben, was three hundred and seventy-nine
years old. His beard covered so much of his face he seemed always to
be peering over a gray cloud. On the little farm, while Taran and Coll
saw to the plowing, sowing, weeding, reaping, and all the other tasks
of husbandry, Dallben undertook the meditating, an occupation so
exhausting he could accomplish it only by lying down and closing his
eyes. He meditated an hour and a half following breakfast and again
later in the day. The clatter from the forge had roused him from his
morning meditation; his robe hung askew over his boney knees.
The villain is the Horned King, who frightens Dallben’s “oracular pig” Hen Wen.
“All the better,” said Coll, “for it makes things that much easier. If
you want to be something with a name attached to it, I can’t think of
anything closer to hand. And it is not every lad who can be assistant
keeper to an oracular pig. Indeed, she is the only oracular pig in
Prydain, and the most valuable.”
“Valuable to Dallben,” Taran said. “She never tells me anything.”
Hen Wen’s ensuing flight begins the book.
Hen Wen usually slept until noon. Then, trotting daintily, despite her
size, she would move to a shady comer of her enclosure and settle
comfortably for the rest of the day. The white pig was continually
grunting and chuckling to herself, and whenever she saw Taran, she
would raise her wide, cheeky face so that he could scratch under her
chin. But this time, she paid no attention to him. Wheezing and
whistling, Hen Wen was digging furiously in the soft earth at the far
side of the pen, burrowing so rapidly she would soon be out. Taran
shouted at her, but the clods continued flying at a great rate. He
swung himself over the fence. The oracular pig stopped and glanced
around. As Taran approached the hole, already sizable, Hen Wen hurried
to the opposite side of the pen and started a new excavation.
was strong and long-legged, but, to his dismay, he saw that Hen Wen
moved faster than he. As soon as he chased her from the second hole,
she turned quickly on her short legs and made for the first. Both, by
now, were big enough for her head and shoulders.
began scraping earth back into the burrow. Hen Wen dug faster than a
badger, her hind legs planted firmly, her front legs plowing ahead.
Taran despaired of stopping her. He scrambled back over the rails and
jumped to the spot where Hen Wen was about to emerge, planning to
seize her and hang on until Dallben and Coll arrived.
underestimated Hen Wen’s speed and strength. In an explosion of dirt
and pebbles, the pig burst from under the fence, heaving Taran into
the air. He landed with the wind knocked out of him. Hen Wen raced
across the field and into the woods. Taran followed. Ahead, the forest
rose up dark and threatening. He took a breath and plunged after her.