Unfortunately there's no such thing as quite and easy when it comes to maxing your stats. The steps you need to take to get to this point take a very, very long time. As has been said you need to take out certain Arena Creations, which are unlocked by capturing certain groups of monsters thusforth;
Fenrir (Agility) - Capture three of each wolf-type monster
Pteryx (Evasion) - Capture four of each bird-type monster
Hornet (Accuracy) - Capture four of each insect-type monster
Vidatu (MP) - Capture four of each "magician"-type monster
One-Eye (Magic Defense) - Capture four of each "eyeball"-type monster
Jumbo Flan (Magic) Capture three of each flan-type monster
Tanket (Defense) - Capture three of each armoured-mole-type monster
Juggernaut (Strength) - Capture five of each horned-animal-type monster
Ironclad (HP) - Capture ten of each iron-giant-type monster
Greater Sphere (Luck) - Conquer at least two species (this is done whilst doing the above)
Eater Eater (Fortune Sphere, the only source of these to unlock Luck nodes) - Conquer at least two areas (Capture at least one of each type of monster in a given area)




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