The most time effective way to obtain stars from each mission is to look at the setup from the people that are at the top of the leaderboard. While you may not be able to play with each one exactly there are many tips to stay alive and get the most out of each challenge.
1. LT is your friend. In the options menu make sure to have the auto-lock on setting turned on as this allows you to lock on to enemies if you are hovering over them with your cross-hairs.
2. With the above technique the most effective method to kill enemies is to crouch behind cover and when ready pop up for a few seconds and repeatedly tap LT while burst firing a machine gun. This makes sure that you make the most out of the ammo and health you have.
3. Sensitivity. In this game it is better to have a lower sensitivity so that you can stay looking at something without problems such as swaying past them. If you are playing with the classic health system then you want to pump as much lead into your opponents as possible so you don't take it yourself.
4. Find what works for you. You may prefer being cautious and taking the enemies out one by one or as a whole group. I have found that both techniques work as you typically take less damage when picking people off but you catch people by surprise when you run straight on at them. This way is quicker but may not be great for harder settings.
Alternatively there is a cheat code you can enter in the Extras menu from the home menu. Type in the word "quimbecile" to automatically unlock all 44 stars in challenge mode. You will get all 3 star related achievements worth 80G after completing one challenge to refresh the game. It doesn't matter if you win as long as you finish a mission.