Welsh constructs the possessive/genitive simply by putting the possessor directly following the thing possessed:
- car Dewi - Dewi's car
- car newydd sbon Siân - Siân's brand-new car
- pensil fy chwaer - my sister's pencil
- cadair goch newydd sbon fy mrawd hŷn - my elder brother's brand-new red chair
To emphasise something in Welsh it is simply put at the start of the sentence. Here, we want to emphasise that Megan's job is part-time (not full-time), so rhan amser is put first.
This is usual when describing names, occupations, relationships etc ('identifications', if you like) but it is commonly used to give emphasis to other elements as well.
If it helps, the two elements separated by yw/ydy in identification sentences are always going to be something nominal: nouns, pronouns, numerals, adjectives, verbnouns (in their nominal capacity). It's never anything verbal like verbs, adverbials or verbnouns (in their verbal capacity) - these all take mae.
So in this case rhan amser acts likes an adjective:
Rhan amser yw swydd Megan "Megan's job is part time"
Hon yw swydd Megan "This is Megan's job"
Gwerthu hufen iâ yw swydd Megan "Megan's job is selling ice cream"
Am dri mae swydd Megan "Megan's job is at three"
Dechrau fory mae swydd Megan "Megan's job starts tomorrow"