you're on the right track.
create 4 variables, something like obj_01, obj_02, etc. in your init file, set them all to false.
when an objective is completed, set the corresponding variable to true.
finally, in your 'friendly guys present' trigger in the base, put the variable check into the condition field, thus:
this and obj_01 and obj_02 and obj_03 and obj_04
that means the trigger will only fire if there's one of the friendly loons present, and all 4 objectives are completed.
hope that helps