This is only partly в шутку ("in jest")!
Learning to distinctly pronounce the hard and soft variants Russian consonants can be difficult for foreigners -- especially English speakers.
But I might suggest that if you want to improve your soft consonants, you might look up "Carol Channing" on YouTube. Here she is performing the song "Diamonds are a Girl's Best Friend" (which was first made famous by Channing herself in the 1949 Broadway musical Gentlemen Prefer Blondes).
Ms. Channing was not Russian, did not speak with a Russian accent, and as far as I know, she had no Russian background (she was born in Seattle). But for some reason, she always had a tendency to "over-soften" many of her consonant sounds. Not only does this make it easy for comedians to do a funny Carol Channing imitation, but it may also help you understand hard/soft consonant pronunciation a little better.
For example, most English speakers pronounce the first syllable of "diamonds" like дай- (with a relatively "hard" D), but Channing says it more like дяй- or дьяй-(with a very "soft" D). Also, listen to the way she says the "b" in "best", and the second "n" in "may be quite continental" -- again, rather close to a "soft" Russian б and н.
And her she parodies her famous role from "Hello Dolly", singing to a Muppet snake on "Sesame Street" -- listen to the way she says "so" at the 0:52 mark. The "s" is softened, and closer to сё than to со, in my opinion. (Между прочим, змею "Сэмми" озвучил Джим Хенсон.)
Thus, you may be able to improve your pronunciation of soft consonants by adding just a little bit of a Carol Channing impression!
But don't overdo it and try to talk exactly like Carol Channing.
Because, (1) if you're a male, it will sound rather gay, and (2) to repeat, Channing didn't actually have a Russian accent, and (3) her vowel-pronunciations were also quite distinctive, and I'm only talking about her consonants.
However, her consonants often had a soft, Russian-like quality, as though she were putting a ь after them. So, watching some Carol Channing videos will NOT give you perfect Russian pronunciation, but it may help take you a step or two closer in the right direction, towards reducing your английский акцент.