Hi Shubham

Double immuno-stainning is very sensitive and complicated, so i suggest you must standardize the conditions of each stain separately (specially Bdru) then perform them as a dual-stain to obtain the best result.

You must know the criteria of each reagent, such that Brdu is used to detect the proliferating cells, while Neun not.

The trail is very hard, but the result will be great.

I hope you will find the following links helpful

Good luck

https://www.google.com.eg/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwiBu_SStOPNAhVB7xQKHbF0D30QFggfMAA&url=http%3A%2F%2Fwww.abcam.com%2Fprotocols%2Fbrdu-staining-protocol&usg=AFQjCNFHf_QyPSqKEq3DxQDWz1_fCj1S4g&bvm=bv.126130881,d.d24

https://www.google.com.eg/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwjamtPcsuPNAhVHUhQKHWX9AZwQFggfMAA&url=http%3A%2F%2Fwww.ihcworld.com%2F_protocols%2Fantibody_protocols%2Fneun_chemicon.htm&usg=AFQjCNGc55w9JLnF0m-l64mlMhuD3VzaeA&bvm=bv.126130881,d.d24

https://www.google.com.eg/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0ahUKEwjamtPcsuPNAhVHUhQKHWX9AZwQFggnMAE&url=http%3A%2F%2Fwww.abcam.com%2FNeuN-antibody-Neuronal-Marker-ab128886.pdf&usg=AFQjCNERFPO0kOTUgX27J2LyFYjyI3tZ9A&bvm=bv.126130881,d.d24

I don't know that it is complicated, just incredibly tedious. BrdU staining normally necessitates using some harsh antigen retrieval to "open up" the DNA and allow the BrdU-antibody to find it's antigen. The trick here is find an antigen retrieval that works for BrdU and doesn't destroy the NeuN antigen in the process. 

The most common antigen retrieval options for BrdU are  DNase & Trypsin  treatment, microwave treatment, and acid treatment. I've only gotten good results with the acid treatment--typically 4N HCl at 37C for 15 minutes for tissue sections but 10mM sodium citrate pH 6.0 at 95°C for 15 minutes sometimes works for tissue culture (details here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3824035/). Other considerations: (1) Sometimes the HCl treatment will cause issues with DAPI and other nuclear counter stains so be thinking ahead about how you will deal with that if you are going to be presenting images as part of your study. (2) Sometimes 1-2% Sodium borohydride in PBS 10-30 mins after acid antigen retrieval can get your other antibody to work--not sure why since this is supposed to reduce free aldehydes and lower background but sometime it works. 

If you can afford it I recommend using EdU (https://en.wikipedia.org/wiki/5-Ethynyl-2%27-deoxyuridine) rather than BrdU. It is super expensive in comparison but the EdU "secondary" is a small molecule and usually doesn't require any antigen retrieval. Before you balk at the price of the EdU kits seriously think about how much time and material resources you will spend optimizing the BrdU+NeuN protocol with no guarantee that you will even find a combination that works. 

Good luck.

Also, by primary brain culture, do you mean a primary cell culture or a primary tissue culture? If you're doing organotypic slices, I've attached a link to a protocol that has worked quite well for me. I've used it successfully for NeuN, but never with BrdU. Is this what you're looking for?

http://www.nature.com/nprot/journal/v1/n5/full/nprot.2006.180.html