How to hear tones in speech better
It will come with more exposure. Watch movies/shows, listen to music, talk with people via voice-chat or in person. 

One of the ways I trained myself to recognize the tones is to listen to the same tone, but with different sounds. 

For example:
biao1 shen1 zhong1 ying1 then he2 ma2 qie2 liu2 etc. 

I found this was really helpful when trying to become more familiar with how each of them sound. I also used this when I started practicing the actually production of words.

Don't give up! Eventually it'll come with exposure and time.