"My duck is tasty."

Translation: Moja kaczka jest smaczna.

[YariMsika]

Duo! how many times have I told you that it's not OK to eat your friends!

[VickIarochinski]

biedna kaczka

[Mr.Xee]

Are we obliged to use "jest" here? Can it be omitted?

[Jellei]

No, it can't, it wouldn't make any sense grammatically.

You can sometimes omit 'jest' in sentences like "This is X" (To jest duży pies vs To duży pies), but it's hard to say when it's perfectly okay and when it sounds strange.