"All I need" is used when you want to express the fact that what you need isn't much. You might say:
- "All I need is one more minute!"
- "All you need is love!"
"What I need", on the other hand, is used when you're simply trying to explain what you need, not how important the thing(s) are. You could have a list, or be in a position where what you need is irrelevant, all that matters is that you get something done, for example.
- "What I need is some diamonds, seventeen emeralds, and a couple of rubies if you have them."
- "I'll need several million pounds."
- "What I need is some more time."
So, in summary, use "all" when you want to emphasize that you don't need much, and "what" when you just want to tell someone what you want.