English Translation
When you feel stressed, take a moment to breathe deeply.
As far as I can find, „durchatmen“ already implies „tief“? DWDS’s definition is literally „tief atmen“.
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The “tief” makes it extra deep… 
Yes, “durchatmen” kind of implies “tief”, but it’s really more about conscious breathing to free your lungs and/or your mind - or to “catch a breath” as in “Keine Zeit zum Durchatmen!”.
It’s basically a set phrase.
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Like @pitti42 said, the “tief” is already implied, but if you explicitly add it, it adds extra emphasis.
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