Consider the simple sentence:
[This picture].NP.sbj [deserves].V [a big like].NP.obj
The more complicated construction that the OP is trying to form is a case of object-fronting, so the object is "moved" with respect to the simpler sentence to the first linear position, and the original object slot is left empty:
[What a big like].NP.obj [This picture].NP.sbj [deserves].V [ $\o$ ]
A number of constructions in English involve dislocating an object noun phrase to the beginning of the clause.
The first proposed sentence ("what a big like deserves this picture") additionally inverts the order of the subject noun phrase and the verb. In many languages where a subject noun phrase would normally precede the verb, e.g., Spanish, subjects may be emphasized, or focused, by dislocating them to appear either after the verb, or after the verb and the object. For example (in Spanish),
Vio una pelicula mi mama.
saw a movie my mother
"_My mother_ saw a movie."
To focus a subject in English, however, no such construction is available, whether in a main or a subordinate clause. So if in your native language you can be flexible about the placement of the subject NP, do not expect to have the same liberties with English.