AN ACR FREIGHTER CLBS ABOVE THE ASSIGNED MISSED APCH ALT AFTER A WINDSHEAR ALERT PROMPTED A MISSED APCH AT PVD. FO; PF; SAYS SHE WAS 'UNPREPARED.'

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AT APPROX 800 FT HAD A WINDSHEAR WARNING; EXECUTED MISSED APCH. EXCEEDED ASSIGNED LEVELOFF ALT OF 2000 FT BY ABOUT 400 FT. DSNDED BACK TO 2000 FT; NO INCIDENT. SUPPLEMENTAL INFO FROM ACN 393747: WINDS WERE FROM S; 15 KTS GUSTS TO 25 KTS. PWR REQUIRED TO MAINTAIN AIRSPD WAS 50%-75% ABOVE NORMAL. TURB WAS MODERATE. AT APPROX 900 FT MSL (850 FT AGL) A SUDDEN LOSS OF APPROX 10-15 KTS AND 'WINDSHEAR' WARNING SOUNDED. ALTHOUGH AIRSPD HAD STABILIZED; I EXECUTED WINDSHEAR RECOVERY PROC PER ESTABLISHED PROC. I WAS PREOCCUPIED WITH FLYING THE ACFT AND THE ALT ASSIGNMENT DID NOT 'REGISTER' WITH ME. I BEGAN THE 'CLEAN UP' (FLAP RETRACTION) BUT PASSED THROUGH THE ALT; CLBING TO 2300-2400(?) FT BEFORE REALIZING (WITH THE CAPT'S PROMPTING) THAT I WAS ONLY CLRED TO 2000 FT. I IMMEDIATELY RETURNED TO 2000 FT. THE NEXT APCH WAS IN SIMILAR CONDITIONS THOUGH NO 'WINDSHEAR' AND ENDED IN A NORMAL LNDG. WHILE I EXECUTED THE WINDSHEAR RECOVERY CORRECTLY; I COULD HAVE DONE IT MORE RAPIDLY AND PERHAPS PREVENTED BECOMING PREOCCUPIED HAD I PROPERLY BRIEFED FOR WINDSHEAR DURING THE APCH BRIEFING. DISCUSSING THE POSSIBILITY OF IT WITH THE WINDS AS THEY WERE; AND REVIEWING THE RECOVERY PROC 'JUST IN CASE' WOULD HAVE PUT ME IN A MORE ALERT MENTAL STATE; FREEING ME TO STAY ON TOP OF THE WHOLE SIT. (A CONTRIBUTING FACTOR MAY HAVE BEEN FATIGUE; AS THE EVENT OCCURRED AT THE END OF AN 11 HR DUTY PERIOD.)