In Pathfinder: Wrath of the Righteous, effectively engaging various enemy types such as demons, undead, and cultists necessitates a thorough understanding of their unique characteristics, resistances, and weaknesses. Here’s a detailed plan for handling each enemy type in combat:

Handling Demons
1. Weapon Selection: Demons often possess resistances or outright immunities to weapons unless they are crafted from special materials. Equip weapons made of cold iron or those that are good-aligned to ensure you are dealing effective damage.

2. Debuffs and Control: Leverage spells and abilities designed to debilitate enemies. Spells that lower their saving throws or impose various debuffs (such as reduced attack rolls or damage) can tilt the odds in your favor since demons generally have strong saving throws.

3. Maximize Critical Hits: Seek to land critical hits, as they allow for substantial damage output. Utilize weapon features or feats that increase the chance of confirming crits, particularly if they involve specific attack rolls.

4. Avoid Fire and Poison: Given their typical immunities or resistances to fire and poison damage, ensure your damage types diversify to include elements demons are less likely to resist.

Handling Undead
1. Avoid Mind-Control and Poison Effects: Undead are usually immune to mind-affecting spells and critical hits. Steer clear of using these types of abilities to conserve energy and resources.

2. Utilize Positive Energy: Exploit the vulnerability of undead to positive energy damage. Classes like clerics and paladins can employ healing spells not only to heal but to damage the undead effectively.

3. Turn Undead: Utilize abilities such as turning undead, which can incapacitate enemies or force them to flee, rendering them less of a threat.

4. Special Weaponry: Consider using weapons with specific enhancements (such as silver) when engaging undead types that might have resistant physical defenses.

Handling Cultists
1. Dispel Magic: Cultists may enhance their power through spells or summon demons. Be prepared with dispel magic or interrupts to break their casts.

2. Area Control: Use crowd control abilities and area-of-effect spells to manage multiple cultists simultaneously. This approach can quickly reduce their numbers, thereby minimizing the threat of summoned creatures.

3. Focus Fire: Cultists generally present less overall resistance compared to other enemy types, so concentrate attacks on them to eliminate threats before they can bolster forces with spells or summons.

General Combat Tips Across Enemy Types
– Combat Mode: Engage your combat strategy using the real-time with pause feature or opt for the turn-based mode to meticulously plan your moves and gains better battlefield control.

– Analyze Resistances: Stay vigilant about each enemy type’s resistances and weaknesses. Choose your arsenal (both weapons and spells) wisely to exploit these discrepancies.

– Maximizing Actions: Make the most of your action economy. Use abilities that allow full attacks or take advantage of feats like Rapid Shot or Flurry of Blows to enhance your damage output per encounter.

– Status Effects: Knowledge of which status effects enemies are vulnerable to can shift combat dynamics. Utilize spells and abilities that inflict such effects strategically to weaken your foes.

Conclusion
In summary, successfully navigating battles against demons, undead, and cultists in Pathfinder: Wrath of the Righteous hinges on adapting weaponry and magical assets to exploit specific weaknesses, while employing tactical maneuvers for positioning and timing. Understanding each unique enemy type and preparing accordingly can significantly enhance your effectiveness in combat.