One idea that would work well with this would be that bosses can't be killed by normal weapons. Instead the player has to utilize the environment to defeat and delay the boss.

For instance let say a boss is chancing you through a bio lab. You can seal it in a feezer by shooting a tank of liquid at the right moment, which will stop to boss for 5-7 minutes. Giving you more time to explore the lab and try and find what you are looking for or a way to stop it once and for all.

Be a total bastard to your player and have a breakable wall on the other side of town from where you meet the boss. Only the boss can break that wall and behind that wall is a super secret that everyone wants.

While the idea of having a monster boss chase you is scary intially it's not exciting and after awhile becomes monotonous.

Try having the monster following the character through cutscenes and things like that while the main character continues on it's quest. This will foreshadow the eventual encounter and when done right will cause fear in the plar, knowing that they are being hunted and will have to evntually face it.