I have been a Psych RN for about 4 years now and my first job was as a new grad. The best bet you have is to look to rural and underserved areas as they are usually desperate for full-time/core Psych RNs. Rural facilities largely rely on travel nurses for staffing.
I would discourage a new grad nurse from applying to a very large hospital, state hospital or prison/jail. Due to the inherent bureaucracy, you will likely get lost in the shuffle and, if hired, your training and mentorship will likely be subpar.
For your interview, be prepared to answer:
Why you want to be a psych nurse as a new grad
The difference between typical and atypical anti-psychotics
What mood stabilizers are and what is their purpose
Different families of anti-depressants
Different anxiolytic drugs
Be able to discuss positive and negative symptoms of Schizophrenia, Bipolar I and Bipolar II disorder, Schizoaffective disorder, and Borderline personality disorder.
What are hallucinations, illusions and delusions (grandiose, paranoid, hyper-religious, persecutory)
What are risk questions (Suicidal/Homicidal ideation; Auditory/Visual/Tactile/Olfactory/Gustatory hallucinations; Depression and Anxiety)
How you would de-escalate a patient in crisis -- e.g. address pt by his/her name; ask what needs are not being met; if what they want is unreasonable/against policy, offer alternatives; change of environment; ventilation of feelings; 1-to-1 counseling, limit setting, etc.
What meds would you ask a physician or NP for in a crisis -- B52 (Haldol 5mg, Benadryl 50mg, Ativan 2mg)
When to use seclusion (danger to others) vs mechanical restraints (danger to self).
Common side effects of psych meds such as Extrapyramidal Symptoms (EPS)/Pseudo-Parkinsons, Tardive Dyskinesia, Stevens-Johnson Syndrome, Serotonin Syndrome, Oculogyric crisis
How to treat and document a seizure and different kinds of seizures
If you can answer all of the above then there is no reason your shouldn't land that job following the interview. Best of luck!