Minecraft wiki entry for Things_not_to_do, associated text: Milk (optional, but can get rid of the mining fatigue effect for a few seconds or after the player kills all the elder guardians). Milk is useless in Bedrock Edition because Mining Fatigue returns instantly after drinking milk.
TNT, some solid blocks, and redstone blocks (optional). This can be used to blast into the monument by placing the TNT against the side or top of the monument, surrounding it with blocks, and placing the redstone block nearby to power the TNT.
An iron or better hoe to break the sponges if they generate (optional)
Various potions are useful: Water Breathing, Night Vision, Invisibility, Instant Health I or II, Regeneration, Strength
A few buckets of axolotls, as axolotls fight guardians and elder guardians. They also remove Mining Fatigue.