Based on current knowledge of this arc, here a summary of the materials needed:
Arc Benediction Brew | Bottled Shadow Dark Compass Enchanted Scissors Troll Spellbook Mermaid Scales Life Flower | Energy
The Academy I 13 | 42 18 22 65 865 | 1 164
The Academy II 70 | 235 51 50 350 4 630 | 6 078
The Academy III 50 | 185 35 65 250 3 340 | 4 485
Total 133 | 462 86 18 137 665 8 835 | 11 727
Collector 134 | 466 87 19 138 665 8 901 | 11 821

Assumptions:
Bottled Shadow: 5 (Fangbeast (Spawn: 3; Defeat: 2))
Dark Compass: 3 (Flight Lesson Dragon, Sparkling Mine (Drop rate: 33%))
Enchanted Scissors: 3 (Flight Lesson Dragon, Sawmill (Drop rate: 33%))
Life Flower: 1 (Flight Lesson Dragon, Aspen Tree)
Troll Spellbook: 1 (Flight Lesson Dragon, Troll Camp)

Mermaid Scales and other common materials not taken into account.

That is gonna be a lot of trees to chop! With an average of 7 flowers per tree, that means 1'272 trees to cut! If you have the dragon you get around 10 flowers per day!