Bring a Naul down to low HP (1-10%) and then use your Soultrapper 2000 on it, while standing very close and in front of it. It will recharge every 30 seconds, and has 48 charges. Use up all of your Blank Soul Plates if you can.
The Soultrapper recharges every 60 seconds and has only 12 charges.
Most Soul Plates will earn you 50-100 Zeni if done the normal way. A full-health Naul will earn you about 900, and a low-health Naul will earn 1300-1500.
Request information on "rare fauna" to receive a pop item for that monster.
The Zeni cost for pop items varies with demand, 1000-2500 for T1, and 4000-10000 for T4. You can expect to spend about 80,000 Zeni in total to spawn all 30 monsters, necessitating further trips to the Naul camp.
When you have killed a monster and received its trophy item, you can trade it to Sanraku for a temporary KI, which is expended when requesting a pop item for a monster of the next tier.
Consult the ZNM page for a flowchart of monsters and KI progression.
With Item Level gear, the monsters are very easy to solo, with some exceptions (e.g. Ob). If you choose to fight every monster, this is a great opportunity to complete the Records of Eminence challenges under Content->ZNM.
When you have all 9 KIs from the T3 monsters, obtain the pop items for Tinnin, Sarameya, and Tyger. Talk to Ryo to learn about travelling to the islets, then talk to Sanraku to purchase various salts.
Driven by ambition, yet still haunted by the disembodied whispers that come at the weapon's touch, you have been ordered by Nashmeira in the name of the Empire to harness the seemingly unconquerable power of the mythic weapons.
SPOILER WARNING: Click here for additional details about this story line.