In Order to get this achievment you need to decrease your deafult cold.
Jax starts with the cold at 50 points(balanced).
each emotional dialog option decrases your cold by 1 point and that is the only way to decrease it.
each time you eat elex or elex potion your cold increases by 0.1pt so try to avoid it
overview of all Cold levels:
0 - Purely Emotional (Emotional)
1-10 - Expressive (Emotional)
11-20 - Irrational (Emotional)
21-30 - Spontaneous
31-40 - Intuitive
41-59 - Neutral (Balanced)
60-68 - Dispassionate
70-78 - Mellow
80-88 - Logical (Synthetic)
90-99 - Ice Cold (Synthetic)
100-1000 - Synthetic (Synthetic)
In conclusion, you need to make 40 emotional dialog options to get this one and never drink or eat any elex.