If a good character draw Ivory Sentinel from Adv deck or just end his movement on it- must he take a battle with it?

The Sentinel cannot be evaded. Any evil or neutral character who enter this space during his move must end his movement and encounter this space. It will remaun here until it is killed.

Ivory Sentinel is a monster, so you have to follow the rules for encountering a monster. In short yes you have to face it.