Does it make a difference how many of the Emperor's bonus objectives you complete?
Tie Fighter extended on X-Wing in that it had not only primary and secondary objectives, but also bonus objectives, given out by an advisor of the Emperor.
Unlike the other ones, the bonus objectives are mostly hidden in their explicit form ("Identify freighter X") until completed. You pretty much had to derive them from the briefing and the debriefing (these usually contained some spoilers, assuming you failed the mission). The only hard value you could see was the number of these objectives ("you completed 1/6 bonus objectives").
I find it often quite hard to figure them all out and complete them all. Yet I do try to complete at least some of them and I do rise in the Emperor's ranks.
Does that mean the game only keeps track of you completing at least one on each mission? (Or how many necessary for the advisor to give you a positive debriefing.) Do you rise in the ranks faster if you complete more? Is it worth going through the extra effort to do them all?
Note: of course I am aware that you do not get any real in-game benefits from working for the Emperor at all. The game is from a time when gamers could still be motiviated without these cheap tricks. ;) The cutscenes are the reward, I guess.
I searched and I searched, but I just could not find an answer to this question, and I wish I had the time to play TIE Fighter again, in order to do some original research, but ...
Anyway, the best information I could find is here, near the end of the document. If this is correct, it would indicate that promotions in the Emperor's ranks occur due to your cumulative score, but there is no indication as to whether you must complete a bonus objective in each mission in order to receive a promotion, or if only completing a single bonus objective (in order to start the process) is enough.
If your rank is based on your score, then completing more bonus objectives will cause you to rise in the Emperor's ranks faster, as each objective completed increases your score for that mission.
I am playing the game now and I can tell you that user7429 is correct. The hooded figure gives you the secondary objectives in most cases and the bonus are still shrouded in mystery.
I also believe that the ranks you get with the emperor are tied to your total score and not bonus objectives. The more bonus objectives you find the higher your score, however. I remember the last time I played through the game I never achieved full rank with the emperor because my cumulative score was not very high as using reinforcements decreases your score.
EDIT: Also dying without being recovered by the empire will destroy your score.