BE40 CREW ENCOUNTERED IMC AND WINDSHEAR ON A VISUAL; EXECUTED A GAR.

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THE FLT ORIGINATED FROM IND TO SUA; FL. THE WX WAS LINE OF SHOWERS AND TSTMS (SCATTERED) FOR SUA; FL; AND DIFFERENT CEILING ALTS OF DIFFERENT AREAS. WE GOT TO SUA; FL; AND ENCOUNTERED IFR CONDITIONS AND ASKED PBI APCH FOR MVA; WHICH WAS 1500 FT. WE GOT RADAR VECTORED TO THE ARPT AT 1500 FT AND WE WERE STILL IN THE CLOUDS. 1 MI FROM THE ARPT WE WERE OUT OF CLOUDS AND HAD THE ARPT IN SIGHT. WE WERE CLRED FOR VISUAL APCH. AS WE STARTED TO TURN AND ENTER THE TFC PATTERN; WE WENT INTO CLOUDS AGAIN AND FLEW RIGHT INTO A LINE OF SHOWERS. IT WAS AT THIS TIME THAT WE ENCOUNTERED A VERY HVY DOWNDRAFT (WINDSHEAR) AND STARTED LOSING ALT. WE WERE CORRECTING (95% ON PWR SETTING AND PITCH UP ATTITUDE); WE DECIDED TO GO TO OUR ALTERNATE. WE CONTACTED APCH BACK AND ASKED FOR HDG TO OUR ALTERNATE (PBI). AT THIS TIME; WE HAD LOST 300-500 FT OF ALT AND STILL CORRECTING. THEN WE WERE INFORMED BY APCH THAT WE NEEDED TO BE AT 1500 FT. WE TOLD THE CTLR WHY WE HAD LOST ALT (WINDSHEAR) AND WE WERE CORRECTING. ONCE WE GAINED CTL; WE CLBED OUT AND UP TO 3000 FT (INSTRUCTED BY APCH). SUA; FL; HAS ONLY A GPS APCH WHICH WE ARE NOT APPROVED TO DO. WHEN WE GOT WX BRIEFING EARLIER; THE WX WAS SUPPOSED TO BE VFR TO IFR. WHEN WE GOT THERE; IT WAS IFR. I SHOULD HAVE CHOSEN TO GO TO MY ALTERNATE ONCE I REALIZED THAT AT 1500 FT MVA AND ALSO OUR TFC PATTERN ALT WE STILL DID NOT HAVE THE ARPT IN SIGHT A LOT EARLIER.