I found that the sleeping routine was directly connected to the eating routine. You don't say what your eating routine is, but at this point she should be eating about every 3-3.5 hours, with short play/tummy times then a nap inbetween each feeding. Over-tired babies will fight sleep. Sounds weird, but it is so true and toddlers are worse, so getting a handle on this now will be a great help for you later.
A possible routine could be:
7am (adjust to whatever her normal wake up is)
10-10:30am
1-1:30pm
4-4:30pm
7-7:30pm
10-10:30pm
She may still need a late night top-up to make it through til morning. Just wake her gently at about midnight and give her a quick tummy warmer in the dark and put her right back down. Both of my girls slept about 7/8 hours at night at 4 months. Even my older one that spent her first 3 months screaming her head off at all hours with colic! Once it had run it's course she settled right into a happy routine. I think we kept the midnight quicky until almost 6 months. Since they were eating solids by then they were eating about every 4 hours during the day and able to make it through 10+ hours at night.
It will take her awhile to adjust, but really if you stick it out for a week you will be amazed! After each feeding, we would play a little while (10 mins or so) then cuddle up to get drowsy. I never rocked my kids all the way to sleep (as a matter of fact my younger daughter would never fall asleep while being held!), just until they were very sleepy. I would put them in their cribs sleepy, but awake then just quietly walk out. Sometimes they would fuss a bit about it, but would always settle. If they cried more than 10 mins, I would walk in quietly saying nothing, but shhhh and give them a little tummy rub then walk out again. Those are the hardest/longest 10 mins of your life, but just keep consistent. Once she is down for a nap, she's down. Don't pick her up again until it is just about time for another feeding, just keep going in to reassure her that you are there and she is fine, but it is sleeping time now. I know it's a killer to have to go in every 10 mins for a couple of hours straight, especially when they are crying, but she really needs the sleep and it gets way better within a day or two. This won't be the last time you will have to listen to her complain about something you are making her do for her own good. :o)
If she's awake feed her at about the 3 hour mark (from start of last feeding), if she's asleep wake her after about 3.5-ish hours (4 max). If she's going to sleep a long stretch let it be at night. :o) Try not to let her fall asleep while nursing. If she dozes, stop nursing and wake her up. Take off her socks, unwrap her, kiss her face, change her diaper, whatever it takes. She'll never get completely full if she dozes off, and a full tummy makes for a better nap.
Just stay consistent and do the same thing every day. It should be less than a week before she is happily snoozing!
I would also suggest moving her out to another room to sleep if you have one.
Enjoy your continuing parenting adventure!