Oh poor thing...so exhausting. Have you got a consistent bed-time routine? Ie bath, milk, teeth, book, bed?
If not, I'd implement one. I'd also try putting her to bed earlier, as she may be getting overtired/overstimulated. So you could try bath at 6pm, followed by a cup of warm milk, then teeth, book at 6.30, in bed by 6.45pm.
Then I would say simply don't take her out of the cot. If she's climbing out you may need to get her a bed. Either way, just keep going in and reassuring her if she cries, rub her back, sit next to her - but don't take her out of the cot or into your bed. She needs to get comfortable in her own bed otherwise she'll never sleep through.
If you put her in a bed, you'll just have to quietly keep putting her back every time she gets out. Even if it means your'e doing it 20 times in a row. Stay consistent and be strong and it'll pay off. She needs to know that no matter what she does, you're not going to give in. You could also try a star chart reward system. So if she's been good in the night she gets a little star in the morning - or even a treat of some kind.
Does she still nap at lunch time? If not, you may want to introduce a nap or just rest-time, as again, being overtired by bed time has the opposite effect of sleep! Sleep breeds sleep. And obviously try not to let her nap late in the afternoon as that would effect her night-time sleep.
Good luck!