A DC8 FLC OVERSHOT THEIR ASSIGNED DEP ALT WHILE TURNING TO INTERCEPT A RADIAL. THE FLC CITED A FAST RATE OF CLB (GOOD ACFT PERFORMANCE) AND NUMEROUS ATC INSTRUCTIONS; AS CONTRIBUTING FACTORS.

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OUR FLT WAS CLRED BY ATC TO CLB AND MAINTAIN 5000 FT. TKOF TOOK PLACE ON RWY 34L; AND WHILE TRACKING THE LOC AFTER TKOF; WE WERE INSTRUCTED BY ATC TO TURN R HDG 090 DEGS AND INTERCEPT THE 059 DEG RADIAL FROM SYDNEY VOR. I WAS FLYING THE ACFT; AND TOLD THE CAPT TO PLEASE TUNE AND IDENT SYDNEY VOR; WHILE I TURNED TO HDG 090 DEGS. WHEN LEVELING WINGS; ATC CALLED AND ASKED OUR ALT; AT WHICH TIME WE WERE CLBING AT 5300 FT; WE IMMEDIATELY STOPPED CLBING; BUT WITH THE HIGH RATE OF CLB; WE REACHED 5800 FT. WE STARTED TO DSND TO 5000 FT WHEN ATC ASKED IF WE HAD TFC IN SIGHT. WE SAID YES; THEN HE TOLD US TO MAINTAIN 5500 FT. 30 SECONDS LATER WE WERE CLRED TO A HIGHER LEVEL. TFC; WHICH WAS A HELI; WAS ABOUT 2 MI FROM US. WE HAD IT IN SIGHT AT ALL TIMES. WX CONDITIONS WERE CEILING AND VISIBILITY OK. SUPPLEMENTAL INFO FROM ACN 337505: JUST PRIOR TO ALT EXCURSION; THE FO HEARD AN AURAL WARNING; BUT BELIEVED IT TO BE THE TRIM MOTOR HORN; AS HE (THE FO) WAS TRIMMING THE ACFT AT THAT MOMENT. THE SO DID NOT CATCH THE AURAL WARNING EVEN THOUGH HE WAS FACING THE INST PANEL AT THE TIME THE ALERTER SOUNDED. I WAS READING BACK DIRECTIONS AND TUNING VOR TO JOIN 059 DEG RADIAL. USING STANDARD ATMOSPHERIC TEMP TKOF PROCS; OUR ACFT PERFORMANCE WAS VERY GOOD DUE TO OUR LOW WT AND COOL TEMP. WHEN INSTRUCTIONS WERE GIVEN; OUR CLB WAS APPROX 2500-3000 FPM. DUE TO RATE OF CLB AND INSTRUCTIONS ALL HAPPENING WITHIN A MATTER OF SECONDS; WE MISSED OUR 1000 FT CALL PRIOR TO LEVELOFF.