"That little mouse does not see the big cats."

Translation: Ta malá myš nevidí ty velké kočky.

[snikta]

I missed out the "ty" and was marked wrong but I thought the definite article was not needed here?

[BoneheadBass]

The "ty" in the Czech sentence indicates that there are some particular "big cats" that the poor little mouse isn't seeing. So "the" is needed in the translation.

[DJLimole]

Is mys feminine? Is that why ta mala is used?

[endless_sleeper]

Yep.