FLT CREW OF B767-300 ENCOUNTER TURB AND WX CELLS ON ARR TO ORD. UNSTABILIZED APCH AND GAR RESULT.

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INBOUND TO ORD. APCHING BEARZ; WE HAD TO DEVIATE L OFF COURSE (W) DUE TO WX BUILDUP AT BEARZ. WE TURNED TO A 240 DEG HDG AND ADVISED ATC. WHILE ON THAT HDG; WE GOT A DSCNT FROM 11000 FT TO 10000 FT AND ATC DIRECTED US TO TURN TO 290 DEG HDG TO GET BACK BTWN 2 CELLS. AS WE WERE DEVIATING AROUND THE WX AND ATTEMPTING TO COMPLY; WE DECIDED THAT THE 290 DEG HDG WAS NOT ACCEPTABLE DUE TO THE NEARNESS OF THE 2 CELLS AND BEGAN A TURN BACK TO THE L. AT THAT TIME; WE WERE STRUCK BY LIGHTNING AND BEGAN A MORE AGGRESSIVE TURN AWAY FROM THE WX TO THE L AND DSNDED TO 9500 FT DURING THIS DEV. IMMEDIATELY; THE CTLR CLRED US TO 7000 FT. (DUE TO EXCESSIVE AIRSPD OF 300 KTS; WE ACTUALLY CLBED TO 10300 FT WHILE BLEEDING OFF THAT SPD AND THEN RESUMED DSND TO 7000 FT -- WX WAS DEFINITELY A FACTOR INFLUENCING ACFT ALT AS WE WERE ENCOUNTERING A WINDSHEAR ASSOCIATED WITH THE CELL.) THE CTLR BEGAN GIVING US ADDITIONAL VECTORS THAT WE WERE UNABLE TO COMPLY WITH DUE TO THE WX AND WE INSTEAD ADVISED HIM ON THE HDGS WE NEEDED. AS SOON AS WE WERE ABLE TO COMPLY WITH HIS INSTRUCTIONS; WE DID; AND INFORMED HIM OF OUR ACTIONS. OUR DEVS CAUSED US TO HAVE A VERY TIGHT DOWNWIND FOR THE RWY 9R APCH AND WHEN THE CTLR TURNED US TO INTERCEPT RWY 9R LOC; WE WERE HIGH AND TIGHT. WE ATTEMPTED TO GET DOWN TO PROFILE; BUT WERE UNSTABLE AT 1000 FT WITH TOO MUCH SPD AND ABOVE GS. WE EXECUTED A GAR AND WERE VECTORED AROUND FOR THE ILS ONCE AGAIN TO RWY 9R. THIS TIME; WE WERE ABLE TO FLY A STABILIZED APCH AND BROKE OUT AT MINIMUMS (200 FT OVCST) AND CONTINUED TO LNDG. THE CAPT AND I HAD A VERY CONSTRUCTIVE DISCUSSION ON WHAT WE COULD HAVE IMPROVED ON. WE AGREED THAT WE SHOULD HAVE BEEN MORE AGGRESSIVE INITIALLY WITH ATC DISTANCING OURSELVES FURTHER AWAY FROM THE CELL RATHER THAN TRY TO ACCOMMODATE ATC. ALTHOUGH WE BECAME VERY PROACTIVE AFTER ENCOUNTERING WX; IT WOULD HAVE BEEN INFINITELY BETTER TO DO THAT BEFORE THE WX. FATIGUE AFTER FLYING ALL NIGHT MAY HAVE INFLUENCED OUR COMPLACENCY TO ACCEPT ATC INSTRUCTIONS INITIALLY. SUPPLEMENTAL INFO FROM ACN 617408: WE TRIED TO CONFIRM THE SAME CLRNC VISUALLY THE CORRIDOR APPEARED THAT IT WOULD REQUIRE A 360 DEG HDG TO GET THROUGH. AS WE GOT TO THE END OF THE FIRST CELL AND USED HDG SELECT TO GO FROM 260 DEGS TO 360 DEGS TO TURN RADIUS WAS INSUFFICIENT TO MAINTAIN DISTANCE FROM THE MOST NORTHERLY CELL. I DISCONNECTED THE AUTOPLT AND INCREASED THE TURN TO 30 DEGS TO TRY AND GET INTO THE CORRIDOR; BUT WE IMMEDIATELY TOOK A LIGHTNING BOLT. I THEN ABANDONED THE TURN AND TRIED TO GO BACK L TO CLR THE NORTHERN CELL. WE ENTERED THE NORTHERN CELL AND GOT INTO SHEAR AND I LOST 500 FT. WE TOLD ATC WE HAD TO COME BACK TO THE L AND HE CLRED US TO 7000 FT. I THINK THE LIGHTNING BOLT SHOOK ME TO THE POINT I HAD SLOWED REFLEXES AND I GOT BEHIND. ALSO THINKING ABOUT TRYING TO COMPLY WITH ATC AND GO BTWN 2 CELLS WAS A BAD DECISION.