To effectively hunt the Beguiler, it's important to first study its behavior. Know when it's likely to use its beguiling abilities.
When hunting the Beguiler in Monster Hunter Stories, start by scouting the area where it is known to reside. Look for signs of its presence like tracks or marks. Once you've located it, keep your distance at first and observe. Try to figure out its patterns. As you engage in battle, stay mobile and don't be easily distracted by its beguiling tricks. Use ranged attacks when possible as this can keep you at a safer distance while still dealing damage. If it uses illusions to disappear, rely on your other senses and the information provided by your equipment and allies to anticipate its next move.
Equip yourself with items that can counter its illusions. For example, some special potions might help you see through its deceptions. Also, bring a monster ally that has good sensing abilities. Team up with it to detect the Beguiler's true location when it tries to hide or mislead. And always be on guard for its sudden attacks as it may feign retreat only to strike back more fiercely.