you get 1 Ancient mana everytime you defeat any of the incarnation of manas. As for the tier 3 challenge of the arena,i'm not exactly sure of the unlock conditions, but it's either defeating the 4 incarnations of mana, or defeating the mother of all life, or completing the pagadol questline.
If you're looking for the items REQUIRED to fight the incarnation of manas, then you need the mana-calling seeds. You can make those using the skill Alchemy from the alchemist class (you might need to obtain a high enough alchemy recipe though).
A tip for fighting the incarnation of manas: if you're having a bit of trouble, try getting some of the gears from the great arenas. You can repeat tier 2 challenges until you get everyone a hat of the strong/cloak of the strong + shield of the strong, and whatever weapon that fits their class.
(I recommend the dagger for DPS class, book for your healer, sword for your tank, and staff for your mage).
The other half is building your classes properly. Melee DPS should pick up +atk passives from the striker and queen class, and all the skills from the top of the mechanic class (breaker drill,chain blade,megaton arm.) If you have enough skill points leftover, pick up the +5% crit and +20% crit from the assassin class. Finally, switch to the dark lord class for passive increased dodge chances (and overall better average stats for boss battles).
Sword is useful for your tank because you can pick up cure slash in the warrior tree and have her support too. Your tank should also pick up incite from the nightmare or valkyrie class. I prefer to have my tank as a valkyie class because of overall decent stats and high defence/stats.
I built my healer to also be a debuffer. It's especially useful to pick up corruption from the nightmare class (sets enemy defense/magic defense to 0 for 1 turn, has a 10 turn cooldown), because along the way you also get +mdef bonuses. All the heal skills in the acolyte classes scale off mdef,so it makes your heals better too.
