I am having the same trouble obtaining a higher rating as some of the other users.

As I understand time has no effect.
How is it that I can obtain a higher rating other than Panawan Learner?

Does it involve obtaining all items on the level and helping all people requiring assistants?

Do I also have to kill every foe I come across?

Here's a post from Jedi72:

I finished the game and reached Jedi Master a couple of times. I only died once or twice throughout the whole game. I think that determines your final rankings. I killed most of the enemies I encountered. Except for level 2. I avoided alot of battle droids there. Anyway here is how I finished 4,5,6,7,8,9,9,9,9,9,9, 2h 24m 48s.
Jedi Master.(pc version)
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Jedi72 has, I think, the correct format to get the Jedi Master ranking. Your ranking is obtained by your score at the END of the game, not an average of the scores of all your levels. My recollection is that you don't get a numeric ranking at the end; just a final "worded" ranking. I could be wrong on this though. So, to get a Jedi Master ranking, you see in Jedi72's post, his ranking number grew each level until he hit 9, which is the highest you can go. And, on the Final Battle level, he RETAINED his 9, so he received a Jedi Master ranking. If your score went from 9 to 8 because you died two or more times (falling off the rings, maybe?), you would get a Jedi Knight (or lower, if you died/restarted more) ranking. But, since the number for the Final Battle level isn't seen, it would look like you finished with a 9, when in actuality you received an 8.
The PSX version works the exact same way. The ranking from level to level works EXCLUSIVELY on the number of times you restart the level or load a savegame; due to death or if you're just unhappy with how you did in a certain area. Number of enemies killed/secrets earned etc. etc. are not calculated in your ranking.