DD (8months now) used to only fall asleep on the boob and if she didn't it could be up to an hour of rocking and crying. And hours through the night too. I was in a real state.
I deliberately broke the feed connection by starting a little bedtime routine.
At about 6pm she got a bath, little massage while I moisturised her, then between 6.30 and 7pm I take her upstairs to bed and BF her. I don't let her suckle for comfort. If she stops swallowing, I sit her up leaning against me and read her a story (Snuggle Bunny in our case). The story is dragged out with improvisations until she starts making sleepy gestures (anything like eye rubbing, stretching, tossing head, ear pulling etc). The story is rapidly finished, then I stand before the window and we wave goodnght to everything outside and slowly calmly shut the blinds. I then sit back down with her and gently rock her and cuddle her and kiss her head (but sitting, not standing) and I have our little seahorse playing tunes on her lap. I keep telling her its time to sleep and softly say sshh shhh. She twiddles with the seahorses fins and tosses her head around a bit. The moment she rubs her eyes hard or stretches, I take her to her cot and lie her down. She has a sleepytot bunny in there which she reaches for. No conversation or eye contact at this point. I then walk out the room and leave her with the seahorse playing out its tunes at her feet.
If she cried I'd go back in and revert to old fashioned rocking.
The first time she went to sleep by herself (it was a while before she did it - not that long though) without me needing to go back and rock her, I was utterly gobsmacked and thought it wouldn't happen again. But it did, every single night without fail since.
She now gets very sleepy almost as soon as I start the story.
However she did still wake through the night and we couldn't self-settle her the same way in the middle of the night.
What I did here was introduce one bottle of formula in the middle of the night whenever she woke up, and DH gave it to her so she didn't smell me. (This was actually on paed advice because I was staunch BF and she had tummy problems - I would never have done it unless told to by a Paed and boy, do I wish I'd started it when we started solids!)). On desparete nights when she woke several times, DH would either rock her, or we'd relent and I'd give her a quick feed to get her back to sleep. I continued to BF as usual when she woke up, through the day and that last before story feed.
We did not wake her for a feed - she only got it if she woke and asked for it so the time varied. It could be 11pm (we never gave it earlier than that) or it could be 2-3am). We were just at the point when we were wondering if she was now waking because she had become used to calories in the night, and wondering if we needed to start cutting down the feed to wean her off it, when - ten days ago - she suddenly slept through the night! So she had no feed that night, and we decided to not give her formula in any subsequent nights if she woke up. To date (touch wood) she has slept through every night so formula is out and I'm back to BF'ding - but now none of the feeds are linked to sleep.
A couple of nights ago we woke to hear her playing with toys in her cot in the middle of the night, and sort of whinging quietly - not crying. We really didn;t know what to do - but decided to leave her. She just went back to sleep. So that's the way we'll play it going forwards as well.
(Daytime naps are our next challenge - at the moment only if she's in the pram, car or being held!).
I have no idea why the routine worked, but I think it is about an hour of totally relaxing very calm time for her, so she gets very very chilled which is key to relaxing her before sleep. I've also wondered if - accidentally - her sleepytot bunny in her cot is seen as an extension of snuggle bunny who she enjoyed in the story. I also think that I enjoy that time with her, so she picks up on that too.
I did not do 'cry it out' or anything close to it - simply could not do it and was in a state because was starting to think that would be my only choice. I think my advice would be to try be calm and very patient about it, and believe in your heart that it will happen eventually, and stick rigourously to your calm chill out routine every night until it suddenly happens. Whatever she loves and calms her, weave that into the routine. (For example, 'The Solar System' song on Youtube, as well as 'Twinkle twinkle' and 'little Snowflake' (the last two being Super Simple Learning songs) are often played to her before her bath if she seems especially 'unsleepy'. She loves them and they're almost 'hypnotic'.
Very good luck. It will happen!