First, let's start with a declarative main clause:
It's supposed to look like this.
We'll turn it into a question by replacing this with what:
It's supposed to look like what?
But this sort of question is only allowed under special circumstances – for example, if you couldn't hear what someone said, or if you wanted to express incredulity at what they said.
Let's turn it into a normal question instead (an interrogative clause):
What is it supposed to look like ＿＿＿?
We did two things here:
- We moved what to the front of the sentence, leaving behind a gap, which I've marked using an underline. Normally the gap would not be written down.
- We inverted the subject it with the auxiliary is.
We had to do step #2 because this was a main clause; main clause interrogatives are marked by subject–auxiliary inversion, unless the wh-phrase is part of the subject.
In your example, we have the same thing, except it's a subordinate clause:
Is that [ what it's supposed to look like ＿＿＿ ] ?
Subordinate interrogatives are not marked by subject–auxiliary inversion, so the only thing we need to do here is move what to the front. The subject and auxiliary remain in their original order: it's, not is it.
Your version is the same thing, but it omits the subject it:
*Is that [ what ∅'s supposed to look like ＿＿＿ ] ?
Here, the ∅ symbol indicates that something has been left out. However, there is nothing that would allow you to omit the subject here, so your example is ungrammatical.
In this answer, the * symbol indicates that a sentence is ungrammatical.