Maggots have a lot more health than CaterpillarsNMC and can inflict DARKNESS on Aya, but can be handled (more or less) the same way as their lesser-HP brethren. They move around slowly, but rear up to leap/pounce on Aya if they get close enough. Fortunately, they telegraph well in advance what they plan to do, giving the player plenty of time to evade their attacks.
All fire attacks work well, given they will be lit on fire and will take burning damage until they die. Combustion|Combustion at level 3 (or lower with the Ofuda equipped) can one-shot an entire group. If it does not kill them, evade their slow attacks until their HP is depleted. POISON and PARALYSIS attacks works fairly well in disabling them.
Given they are one the rare few NMCs that takes critical hit damage, weapons such as the M93R, P08 and P229 work fairly well if the player can engage them one at a time.
While burning, they can do slightly more damage to Aya if one manages to hit her. If fire is the player's strategy, take extra caution to evade their melee attacks.
Amoebae can also set Maggots on fire. After draining Aya of some MP, their Pyrokinesis-like attack can damage one and set it on fire. This has the added benefit of causing critical damage to any Amoebae they are next to when taking burning damage, killing Green Amoebae outright and heavily damaging Red Amoebae.