"и" is a quite weird sound, it's not easy to explain what it is :) Try to do this: start saying "i" or "ee" in English (as in "weed") but don't press your tongue to the roof of your moth so much, try to adjust it as if you were saying "e"!
Or the opposite: start saying "e" (the Ukrainian one) but make your mouth wide as if you were saying "i" or "ee".
It is sometimes similar to the English short "i" or the sound that you make when you say "the" followed by a vowel (e.g. "the end", "the answer")
When you pronounce a hard "e" in English your tongue is pressing down in your mouth with the tip touching the back of your lower teeth. This is also true of of the Ukrainian "i" but maybe with the tongue slightly relaxed. The Ukrainian "И" I think tongue is off the surface of your lower mouth and not touching your teeth. To me it almost sounds like saying "oy" but with a less pronounced "o".