"We hear my pig."
Translation:Slyšíme moje prase.
You are right, it is accusative when you hear someone or something.. But it is more complicated with accusative. Every noun, adjective, pronouns, possesive pronouns gets right ending which belongs to its gender and its "pattern word")
"Prase" is neuter so pronoun gets neuter accusative ending -e and "žena" is feminine so pronoun gets feminine accusative ending -i.
I hear my pig. - Slyším svoje prase.
We hear our pig. - Slyšíme svoje prase.
You hear your pig. - Slyšíš/slyšíte svoje prase.
Tomáš hears his (own) pig. - Tomáš slyší svoje prase.
Tomáš hears his (someone else's) pig. - Tomáš slyší jeho prase.
If the pig belongs to the subject, use "svůj". Otherwise, do not use it.
"We" and "my" don't match, so the reflexive "svůj" cannot be used here.