to get the skill, you just need the last quest. 

the first quest is Veteran’s Patience. 
Kill 100 sheid weavers. 
lvl requirement: 99-100 
quest rewards: 2.2b exp, 100 sp (without pbi/pssp) 
NPC: Patriarch Zikil (Egeha) 

second quest is Veteran’s Courage. 
Kill 20 akan magic knights, akan shamans, akan therapists. 
lvl requirement: 99-100 
quest rewards: 2.8b exp, 200 sp 
NPC: Patriarch Zikil 

third quest is Veteran’s Trust. 
Kill 100 ancient screaming zombies and 100 ancient grey mummies. 
lvl requirement: 99-100 
quest rewards: 3.4b exp, 300 sp 
NPC: Patriarch Zikil 

last quest is I am the Veteran. 
Kill grand gold dragon, darkmind terrain, and iludeteirun. 
lvl requirement: 100-199 
quest rewards: Veteran Adventurer title, Veteran’s Composure skill book, 9b exp 1000 sp 
NPC: Patriarch Zikil 

the skill book comes at the end of the quest chain, so you need to finish the quest chain to get the skill. here’s the description from the skill book: 
"[Skill Book] A book that contains kowledge necessary to learn Veteran’s Composure. Only one who has passed the test of the Veteran may obtain this" 
the skill book is not tradeable. 

Skill effects: Same for both dual classes, all come with a provoke "massive" monsters near the target and decreases the following attributes: 
Titan: physical defense and attack speed 
Knight: physical defense and attack speed 
Healer: physical and magical defense 
Mage: magical defense and moving speed 
Rogue: physical defense and attack speed 
Sorcerer: magical defense and moving speed 
Night shadow: magical defense and moving speed 

Special thanks to: 
cbigsby 
bladeofchaos09

Credits go to b1ank.