A B739 CREW; ON APCH TO CANCUN; (MMUN) EXECUTED A GAR AFTER AVOIDING TSTM ACTIVITY; WHICH LEFT THEM HIGH AND THE RECIPIENT OF A TCASII TA.

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CLRED TO INTERCEPT ILS RWY 12; DSND TO 2000 FT. ACFT ON GLIDE PATH; GEAR DOWN 240 KIAS. PASSING 3000 FT; WE ENTERED AN AREA OF TCB JUST N OF A RAIN SHOWER ON A 100 DEG HDG. ENTERED LIGHT RAIN AND TURB. HOWEVER; DSCNT BECAME A SLIGHT CLB AND AIRSPD INCREASED APPROX 30 KTS FOR ABOUT 1-2 MI. WHEN CLR OF CLOUDS; POS WAS SLIGHTLY N OF LOC AND FULL GS DEFLECTION HIGH; 2000 FT. FIELD IN SIGHT. I TURNED TO 150 DEGS TO AVOID ONE ADDITIONAL CELL; SEE IF VISUAL APCH PARAMETERS COULD BE ATTAINED. WE HAD NOT BEEN ABLE TO TALK TO APCH CTL BECAUSE OF RADIO CONGESTION TO INFORM OF OUR SIT. AS I TURNED BACK N AND BEGAN THINKING MISSED; APCH CTL CAME ON THE RADIO TO ALERT US OF AN ACFT 2-3 MI S; HEADED AT US; AVOIDING SAME STORM. WE HAD TA WARNING; BUT NO EVASIVE ACTIONS WERE GIVEN OR TAKEN. WE ACCOMPLISHED A MISSED APCH; VECTORED L 270 DEGS TO VISUAL APCH AND UNEVENTFUL LNDG. DURING THIS 8-10 MINS; THE CELL HAD GROWN FROM A 1 MI WIDE SHOWER TO A 5-6 MI WIDE LEVEL 4 TSTM. DURING MISSED; CTLR ASKED US WHAT WE HAD BEEN DOING. FO RESPONDED CAPT USING EMER AUTH TO AVOID WX. I SHOULD HAVE BEEN AT 210 KIAS OR SO WITH SOME FLAPS DOWN; WHEN WE HIT THE WX; BUT IN HINDSIGHT WOULD HAVE OVERSPD FLAPS. THIS STORM LOOKED LIKE HOUSTON SUMMER TCB'S THAT WE WERE AVOIDING THE RAIN; BUT BY NO MEANS EXPECTING THE UPSIDE OF WHAT I'M SURE BECAME ONE INTENSE MICROBURST. SUPPLEMENTAL INFO FROM ACN 556026: TRIED TO CONTACT ATC TO DEVIATE R OF COURSE; BUT WAS UNABLE DUE TO FREQ CONGESTION. CAPT EXERCISED EMER AUTH AND STARTED A R TURN TO AVOID WX.