Which of the following full sentences is correct?
- Our voice needs to be heard by the media.
- Our voice is needed to be heard by the media.
It sounds to me as if they are both the same and giving a passive voice.
This question is better suited to our sister-site ELL (English Language Learners) but in case it doesn't get migrated here's an answer.
"Our voice" is singular, so the verb that follows must be in the third-person singular (Wiktionary)
Our voice needs to be heard
As to your second sentence, which is in the simple present passive voice, it's grammatical but its meaning is slightly redundant.
Our voice is needed to be heard
The speaker is saying their voice is necessary for it to be heard by someone or something, which I suppose makes sense. But I think the OP is looking to say the following
Our voice must be heard
See Google Ngram chart below for confirmation