In short, compared with complete fasting, intermittent fasting results only in a minimal increase in plasma cortisol levels.
Cortisol increase in INTERMITTENT FASTING:
Effects of eight weeks of time-restricted feeding (16/8) on basal metabolism, maximal strength, body composition, inflammation, and cardiovascular risk factors in resistance-trained males (Journal of Translational Medicine, 2016):
In this small study in 34 males, intermittent fasting (16 h fasting/8 h feeding) was associated with an increase of plasma cortisol from 174 ng/mL at the beginning of the study to 186 ng/mL in average after 8 weeks (Table 3), which is 1.07-fold increase.
Cortisol increase in COMPLETE (WATER) FASTING:
Fasting as a Metabolic Stress Paradigm Selectively Amplifies Cortisol Secretory Burst Mass and Delays the Time of Maximal Nyctohemeral Cortisol Concentrations in Healthy Men (Journal of Clinical Endocrinology and Metabolism, 1996)
In this study in 8 males, the 5-day fast resulted in a 2.2-fold increase in 24-h mean serum cortisol concentrations.
Elevated plasma cortisol level can be a part of normal stress response, so the presented studies alone do not suggest that either intermittent or complete fast is unhealthy.