All international students who stay in Japan for three months or more are required to enroll in National Health Insurance. This health insurance covers 70 % of your medical expenses so that you need to pay only 30 % of the actual medical expenses at medical institutions. And by High-Cost Medical Care Benefit, you can get refund of the payment that exceeds the designated amount in the month. When you already know that you will need to bear huge medical expenses, you can get a Medical Payment Limitation Certificate in advance. With this card, you don't need to pay the amount that exceeds the limit. For more details, please inquire at the NHI section of the city hall of your city.
Tsukuba City High Medical Cost Subsidy Program:

https://www.city.tsukuba.lg.jp/kosodate/hoken/kenpo/1004171/1001233.html

Joining and Cancelling

To join the National Health Insurance Program, apply at the NHI section of the city hall of your city. When you move into the city, present your Residence Card and Student ID Card and apply for the insurance along with the residence registration. Note that even if you apply for NHI later, your payment is calculated from the day you moved into the city and you must pay it all.
When you leave Japan, make sure to deregister as a residence, cancel NHI and liquidate the payments. Note that if you leave Japan with any unpaid insurance fees, you will need to pay them when you live in Japan next time.

Insurance Fees (Insurance Tax)

The basic amount of the insurance fee varies depending on the city. In Tsukuba City, the annual insurance fee for those under age 40 is 56,900 yen (as of 2019). However, by reporting your income at the City Tax Division and getting approval that you don't have any income and are exempt from the residence tax payments, your annual payment will be reduced to 17,000 yen. You need to do this income report every year. Scholarship is not regarded as income.

Visa Extension and Insurance Card

When you extend your visa, notify the city hall to make your insurance card also extended. The new NHI card is valid from the day the new Residence Card has become valid. Note that if your Residence Card became invalid while you are waiting for the new Residence Card to be issued, you need to pay 100% of the medical expenses. In such case, you can apply for the refund within two years from the day you made payment. However, if there is any gap between the expiration date of your Residence Card and the approved date of the new card, the insurance does not cover at all the medical payment you made during the gap days. To avoid such a situation, apply for a visa extension as early as possible so that you can get a new Residence Card before the current Residence Card become invalid.

To learn more about the Tsukuba City Medical Services, click here.