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 /əˈtʃiːvd/ I accomplished /əˈkɒmplɪʃt/ 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:
| reach | attain | secure | realise | fulfil | achieve |
an ambition | | ✓ | | ✓ | ✓ | ✓ |
a dream | | | | ✓ | ✓ | |
an agreement | ✓ | | ✓ | | | |
an obligation | | | | | ✓ | ✓ |
a target | ✓ | ✓ | | | | ✓ |
a compromise | ✓ | | | | | |
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 /ˈfɒltə/, 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, my girlfriend's left me; I need help; I can't cope any more.
C ‣ Word formation 
verb | noun | adjective | adverb |
succeed | success | successful | successfully |
accomplish | accomplishment | accomplished | |
achieve | achievement | achievable | |
attain | attainment | attainable | |
fulfil | fulfilment | fulfilling | |
harden | hardness | hard | hard |
Common mistakes
Izzy had great difficulty finding somewhere to live in London. (NOT difficulties)
Paul had considerable success with his first novel. (NOT successes)