by hard strike do you mean X? By conter do you mean Y where the person turns red?
My problem isn't defeating one - it's that they are always in groups and when I start fighting one, others stab or kick me and 2-3 hits, i'm dead. I spend most of my time running around trying to separate them. As for the BIG guys, i have no idea how to defeat them (esp the one whobodyslams you all the time).
I play on the PC, so I use different keys, but by doing hard strikes, you HOLD the X-button. To counter, you quickly press the Y-button when an enemy is flashing red. Unless there is a grappler in the group, you can defeat them by only press Y at the right moment, and do nothing else. It will take forever, but it's possible. Just like in Batman: Arkham-series.
What you should do, is to keep your combos short, like 3 hits, before you start looking for someone flashing red. It doesn't matter that you're surrounded. Just hit a guy three times, then get ready to press Y. When you have countered one, hit 3 more times, wait for a counter. Keep this up.
If there is a grappler in the group, try to kill him first. If you want, I can make a YouTube-video of a massive fight.