What is eradication of the fetter of identity-view (sakkāya-diṭṭhi)?
The ten fetters have the eradication of the identity-view or belief in
  a self (sakkāya-diṭṭhi) as a lower fetter, that has to be done in
  order to become a sotapanna or stream winner.


It's actually the other way around, meaning becoming a stream enterer will be 'done' before the belief in a self is eradicated.

After becoming a stream enterer you'll realise that you are nothing more than a process (for the lack of words).
Before becoming a stream enterer the mind will pick and observe one of the three characteristics: anicca, dukkha or anatta. And when this characteristic is understood/seen completely the mind will release and let go.

And even though the stream winner knows then, from experience, that (s)he is nothing more than a process it doesn't mean that (s)he also experience everything impersonal. Awareness itself for instance will still feel as 'I am aware of this or that'. The difference is between deeply knowing from experience (entering the stream) and experiencing or feeling, or sense of self as you put it.

That sense of self will be eradicated with the uprooting of conceit.