Generally, the first 3 items are very similar. But we can find a bit difference, too:
achieve success, achieve a goal, achieve one's ambition
reach for the sky, reach to, hard to reach
succeed in achieving (something that one desires and has worked for), attain a result
Первые три глагола имеют значение "достигать". Четвертый переводится как "выигрывать, приобретать".
The fourth verb is used in situations like: gain knowledge, gain experience