Explanation
Expresses 'no matter how much...', 'even if...'.
Formation
どんなに + Verb-volitional + うが, どんなに + い-Adjective(～かろう) + が, どんなに + な-Adjective + だろうが
Detailed explanation
The grammar point どんなに～うが is used to express a condition that is not affected by the degree of an action or state. It can be translated as 'no matter how much...' or 'even if...'. It is generally used with verbs, い-adjectives and な-adjectives in their volitional or かろう/だろう form.
Examples
Donna ni ganbarou ga, kare no hayasa ni wa oitsukenai.
No matter how hard I try, I can't catch up with his speed.
Donna ni tabeyou ga, kanojo wa futoranai.
No matter how much she eats, she doesn't gain weight.
Donna ni samukarou ga, kare wa mainichi jogging wo shimasu.
No matter how cold it is, he goes jogging every day.
Donna ni atsukarou ga, eakon wa tsukaimasen.
No matter how hot it is, I don't use air conditioning.
Practice
Grammar content sourced from hanabira.org.