Many studies have been done on the benefits of Tai Chi.  Listed below are some of the articles and links to some studies.

Fibromyalgia

Can Practicing Tai Chi Help your Fibromyalgia Pain?  http://www.fibromyalgiatreating.com/can-practicing-tai-chi-help-your-fibromyalgia-pain/

Tai Chi: Best Fibromyalgia Treatment?   https://www.webmd.com/fibromyalgia/news/20100818/tai-chi-best-fibromyalgia-treatment#1

A Randomized Trial of Tai Chi and Fibromyalgia       https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3023168/

Parkinson's

Parkinson's Disease and Tai Chi: Bringing Balance to the Body  https://parkinsonsnewstoday.com/2017/11/15/parkinsons-disease-tai-chi-and-balance-in-disease-marked-by-falls/

Tai Chi Improves Balance and Motor Skills in Parkinson's Disease  https://www.health.harvard.edu/blog/tai-chi-improves-balance-and-motor-control-in-parkinsons-disease-201305036150

Hypertension and Coronary Heart Disease

The beneficial effects of Tai Chi Chuan on blood pressure and lipid profile and anxiety status in a randomized controlled trial.  https://www.ncbi.nlm.nih.gov/pubmed/14629852

Tai Chi Boosts Quality of Life in Patients with Heart Disease   https://www.cardiosmart.org/News-and-Events/2017/10/Tai-Chi-Boosts-Quality-of-Life-in-Patients-with-Heart-Disease

Tai Chi is a Promising Exercise Option for Patients with Coronary Heart Disease Declining Rehabilitation  http://jaha.ahajournals.org/content/6/10/e006603

Tai Chi Training for Patients with Coronary Heart Disease    https://www.ncbi.nlm.nih.gov/pubmed/18487898

COPD

COPD: Tai chi a 'viable alternative' to standard treatment  https://www.medicalnewstoday.com/articles/321427.php

Tai Chi and COPD  https://lunginstitute.com/blog/tai-chi-and-copd/

Tai Chi Exercise for Patients With Chronic Obstructive Pulmonary Disease: A Pilot Study   https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3280096/

PTSD

Evidence Map of Tai Chi  https://www.hsrd.research.va.gov/publications/esp/taichi-REPORT.pdf

Tai Chi Proves Feasible and Beneficial for Vets  With PTSD   https://www.sciencedaily.com/releases/2016/11/161130131311.htm