A. Succeeding

We succeeded in persuading a lot of people to join our protest. (in + -ing)
I managed to contact him just before he left his office.
I don’t think I can manage the whole walk. I think I’ll turn back. (manage, but not succeed; may have a direct object in this meaning)

We’ve achieved / accomplished a great deal in the last year. (both are used with quantity phrases such as ‘a lot’ and ‘a little’; accomplish is rather formal)
The company has achieved all its goals/aims/targets for this year. (achieve is more common than accomplish with nouns expressing goals and ambitions)
Do you think his plan will come off? (succeed; infml)

Here is a matrix for some typical collocations with ‘succeeding’ verbs:

B. Failing and difficulty

• Plans and projects sometimes go wrong / backfire. [don’t go as intended]
• Companies, clubs and societies often fold / go under through lack of success. [close down; go under is informal]
• A plan or project may falter, even if it finally succeeds. [have ups and downs]
• All your plans and hard work / efforts may come to nothing.

I have great difficulty (in) getting up in the morning.
I find it difficult to remember the names of everybody in the class. (hard can also be used here; it is more informal)
It’s hard/difficult to hear what she’s saying.
I often have trouble starting the car on cold mornings. (more informal)
We’ve had a lot of bother with the neighbours lately. (very informal)
Can you cope with three more students? They’ve just arrived. (deal successfully with a difficult situation)
I’ve got no money and my girlfriend’s left me. I need help; I can’t cope any more.

C. Word formation