Baby night sleeping pattern

In the 0mo (Oct '14) baby slept almost all the time. she only woke up every ~2 hours for feed. Her stomach is so small that it can only hold that much of milk that last for 2 hours max. Occasionally she stay awake whole night because the concept of time did not exist in the womb.
1mo (Nov '14), we finished those few bottles, completely dropped the bottle feed and purely feed direct. Bb sometimes wake up every hour because milk intake from breast directly is more tiring so bb tends to drink less. This the most exhausting month. Mummy is constantly lack of sleep. On average 4 feeds a night.
2mo (Dec '14) onwards bb sleep stretch longer gradually. 4 hours sleep is a blessing to mummy. Average 3 feeds then reduced to 2 feeds a night.
3mo (Jan '15). Bb can almost sleep throughout the night waking up only once. Usually is around or between 3-4am. Her sleeping record so far was 930pm to 545am. But it would be good for mummy to wake up in the middle of night to pump milk to maintain the milk supply.
4mo (Feb '15) we started to sleep train bb. Day time nap is bb guided. She sleeps, eats, plays whenever she likes. Sleeps when tired. But night time sleep we tried to fix it around 9-10pm. So she will have a 6 hour stretch. How to sleep train? All the websites talk about the same thing, put bb down when drowsy but awake. Trust me it is tough to implement. We still have to nurse, cuddle, rock, sing, do all the stunt to make her sleepy. The moment I put her down she either fall asleep quickly or turn wide awake. If she goes zzz, good for us. If she fuss, I'll pat her, sing to her or give her a pacifier. She usually doesn't take pacifier. It's only for sleeping. If all tricks fail, try again. She will eventually get tired and defeated by the zzz monster.
5mo (Mar '15) Her night sleep further stretch to 6 hours long.