Soundproofing DIY Project

As someone said above, retrospective sound insulation is difficult. A lot depends on what you are trying to prevent. Do your neighbours have live bands play next to you or do they just have noisy kids, the hi-fi is turned up, loads of parties etc etc?

With sound, generalising massively, it's split into high frequency and low frequency. High freq is relatively easy to block being highly directional. However low frequency is, by and large, omni directional and very difficult to stop. Most efforts of sound insulation tend to work on the highs, but have no effect on the lows and usually result in a muffled thud, thud thud sound as the low frequencies 'leak' through the joints, joists, or any connecting path, which is why the room within a room principle is the way to go to avoid this, though this is clearly impractical for a house.

It's also worth remembering that the other key is density. In your case mineral wool will have little effect (other than maybe helping your heating bills). You need isolation (a rubber mat across the whole of the area) and density (a couple of staggered layers of thick plasterboard sheets as an example) . But as well as the loft you'll need to think about the walls (the low freqs will leak through them) and the floor (and them), windows (ditto) and doors (ditto) and then you quickly realise it's like trying to plug holes in a colander.

Not trying to put you off, but it's a lot of work and expense, without any guarantee of it working and sometimes it's cheaper, easier and more effective to work with neighbours in mediation to resolve the issues. If you do go ahead with it then you'll need to be realistic about what result you'll achieve.

Good luck.