1Extermination or elimination of pests, harmful things, or problems; getting rid of or suppressing something.
台所に出たゴキブリを退治した。
I exterminated a cockroach that appeared in the kitchen.
害虫退治のために農薬を散布した。
They applied pesticide to control pests.
問題を早めに退治しておかないと大きくなる。
If you don't nip the problem in the bud, it will grow bigger.
2In Buddhism: renouncing worldly desires and attachments; removing defilements to concentrate on teachings or practice.
修行者は欲望を退治することを目指すと言われる。
Practitioners are said to aim at eliminating their desires.
3Curing an illness; getting rid of a disease or symptoms (colloquially 'to beat' an illness).
風邪をしっかり治して、早く退治しよう。
Make sure to recover from the cold and get rid of it quickly.
医師の治療で感染症を退治できた。
The infection was eradicated thanks to the doctor's treatment.