I used to be terrified of hills and would actively avoid them...mind that wasn't hard when I lived in Norfolk
Saying that I got a new bike not long ago with a triple, and did Essex to Bristol this week. Between Newbury and Devizes route 4 takes you away from the flat towpath and over what my friend described as 'undulating roads'...it was certainly harder than he made it sound, but I only pushed up one hill and that was first thing in the morning up gravel where I wasn't too sure if I'd make it. later that day we had a similar gradient but on a road and I gave it a crack and somehow got to the top with full panniers and about 6st overweight. My mind was by far the biggest obstacle, if you believe you can do it then your legs will keep spinning, no matter how slow or what gear you are in. But the moment you begin to doubt is the moment your legs slow down as if to say 'nice one brain, didn't want to say it but I'm knackered!'
Now I know I can actually do hills, albeit in the smallest gear and pathetically slow, the only thing I can do is progress. I now live in Bristol so am trying to map a route around quieter roads with select gradients and climbs in them to practice on. If anyone in Bristol has any suggestions/ideas, let me know !