How did I let his white group on the bottom make two eyes?

How did he slip away or was there anything I could have done to make sure it was killed?

Starting at move 205

You had to atari from the other side, with Q2, to prevent that group from being captured. Then you would keep adding moves from that side if he were to continue extending the stones.

The problem starts earlier than that. For example what is the purpose of move 203?

One of your worst moves is 137. Learn to attack from a distance, as contact moves are usually an invitation for mutual reinforcement:
http://senseis.xmp.net/?AttackFromADistance

Move 221 also looks pretty much useless.