It's good work for a first piece, but there still seems to be some confusion.
For example:
"Are you sure
it's hatching, Laya?" Tamaska asked, watching the cracking egg worriedly.
Correction bolded. You use 'it's' in place of 'it is' in this instance. The apostrophe replaces the missing letters.
"Of course it is
," Laya answered, watching the yellow nose pop out of the egg.
There should be a comma after the word 'is'.
"Cyn!" A small voice came from the small Cyndaquill, now out of the egg. The parents both gasped as they watched the newborn crawl towards them.
This just sounds weird. Would you consider rephrasing?
Laya pcked the Cyndaquill up and said "Its a boy! What should we name him?" she asked, looking over at Tamaska.
You don't really need both 'said' and 'asked' in this instance; one or the other. Also, saying the 'said' before the actual words just looks and sounds strange. You do that multiple times.
"Thats a great name
," She said, cradling the newborn. A few hours later, Rebel fell asleep. Their food supply was low, so Tamaska went off to hunt.
Comma error again.
"Theres got to be more out here then just a Dunsprace..."
he said, sniffing the air. A Tyranitar was trudging around angrily. He caught scent of Tamaksa and started in his direction, ready to release his anger. A little while later,
the beast was upon Tamaska. Tamaska looked up at the beast, eyes narrowed and chest puffed out.
"Fine with me
," Tamaska said. The two circled, then Tamaska jumped him. Tyranitar dodged, then grabbed him. He held a claw to Tamaksa's throat. Tamaska snarled and used Eruption. The move did little to Tyranitar.
"Fine
," Tyranitar said, then slit his throat and dropped him.
Tamaska choked a little, blood pouring out of his throat. The Tyranitar watched him choke for a moment, then walked off. Tamaska
finally bled to death, cursing the Tyrnaitar.
How can he curse when he is dead?
"Stupid rodent
," Tyranitar laughed, walking away.
"Tamaska!!"
she barked, standing and dashed out of the den. Rebel was fast asleep, still in the den. Laya arrived at the scene, and fell to her knees.
"N-no..."
she whimpered, tears streaming down her face. She then stood, enraged. She sniffed the air, and caught scent of Tyranitar.
I think you need to research how to use dialogue at this point.
This might help.
"What the-"
she kicked him in the face, then the
chest. He stumbled backwards and on to his back. Tyranitar roared and fired Hyper Beam at her as he stood, throwing her back and
impailing her on a thick branch. She whimpered and coughed, then used Extrasensory to choke him. Tyranitar held his throat, slowly suffocating. He fell to his knees, and passed out.
She kept suffocating him, until he finally died. She sighed in relief, and half smiled.
The word 'suffocating' doesn't work like that; at least I don't think it does.