Almost perfect. But sentences should be plural and we don't say convicted to a sentence. So here's my suggestion: "Criminals who have committed heinous crimes should be convicted and given long-term sentences"

I'd change the voice to Passive, so it'd be : Heinous crimes committed by criminals should be......

Or you could say: “Criminals who have committed heinous crimes should be handed long-term sentences”

Criminals who have committed heinous crimes should be sentenced to long-term imprisonment.