How to improve my climbing? I can ride on flat at high gears all day without a problem I usually go way faster that most of riders. But once it comes to hills I die... My heart beat rate jump up my stamina go away and I get tired in seconds. Even older folks that barely have any cadence on flat can beat me on hills. I need to get down from my bike , take a break and keep on foot. Because once on bike again my heart rate will go crazy again and I will get tired in seconds.

I am doing something wrong ? I always go to the lower plate and lower cogs on climbs but if it is too steep even the lowest one kills me. 

I drive a lower end hybrid bike. It have I belive 14-28 (7 rings) rear cassette and 28/38/48 front gears. How much it matters compared to how fit you are ? I mean 1:1 relation it is should be more that enough to climb.
Too much info for a comment, I've checked the suggested duplicate and this is slightly different.  This question is about effort and approach, not climbing technique.



Answer You're going at the hill too hard.  Learn to PACE your efforts.

Medical rule of thumb, your maximum heart rate should be 220 minus your age.  I'm 40 so my heart rate should not exceed 180.  However my HRM in strava shows peaks in the high 170s.
So 200 BPM might be a maximum heart rate for a fit 20 year old.

If you're doing decent flat speeds, then don't expect to travel uphill at those same speeds.  I think you're trying to keep the same speed and blowing yourself up.

Instead, find a quiet grade of about 8%, and start by riding up like normal.  Note how high you get before you have to stop.  Then turn around and go down, resting and recovering.

Second time - go up the hill in your bottom gear (that's the small front and the biggest rear cog)  Focus on keeping your pedalling cadence at "normal" and avoid pedalling too fast.  Also avoid bouncing in the saddle, but stay seated.  You will ride slower, but see how high you get before you have to stop.  I bet it takes much longer, but you will well exceed the turnpoint of the first attempt.  And you'll be less shattered passing that point too.

Climbing is all about PACING your effort.