>Not (being) good at swimming, he didn't like it.

There is no problem omitting *being* in such phrases. 

Other examples include 

>[Being] afraid of water, he didn't like swimming. 

>Not [being] good at swimming, he became a boxer.   

See also 12 other example sentences (Numbers 12-23) in [a similar question and answer](http://thegrammarexchange.infopop.cc/eve/forums/a/tpc/f/340600179/m/3441084324) at Azar Grammar Exchange. The first post is the question, and the second post gives the answers to each numbered sentence. 

The only questionable thing about your sentence is the use of *it*. We can't be sure whether *it* refers to 

1 *swimming*  

or to the whole phrase  

2 *Not (being) good at swimming*

Most native speakers would probably interpret *it* to refer to swimming. 

But it is possible for a pronoun to refer back to the entire -ing phrase. Here's one example:

>Although [being] a poor swimmer, he didn't let it bother him. 

*It* refers to the whole phrase *[being] a poor  swimmer.*