Basically, as your father is an EEA national with permanent residence (PR) your father has already proved that he exercised at least five continuous years of Treaty Rights as a worker (or former worker who became sick), so they gave him a document certifying that PR in 2007.
As the non-EEA family member you need to prove five years continuous residence, which is usually easiest starting from the nearest date: so for example your five years continuous residence is:
July 2011 back to July 2006 = five continuous years UK residence. Though you can pick whichever five years suits you best ( most evidence of UK residency).
So, you will also need to prove your father was also resident in the UK from July 2011 back to July 2006 or probably only back to 2007 when he got the document certifying PR had been acquired.
You will also need his passport and your passport and the document which proves that he has PR. You will also need to prove your family relationship ( your birth certificate).
That's the advice I read on before online and it's also what the "European Commission's Your Europe Advice" legal advisers told me too.
If you want, you can write to them and ask them to confirm if what I have written here is legally correct.
The site is here:
http://ec.europa.eu/citizensrights/fron ... dex_en.htm
All the other stuff on the EEA4 form about exercising Treaty Rights: Comprehensive Sickness Insurance, proof of employment, earnings and proof of savings of the EEA national and the many other things they ask for should not apply, cos your father already went through all that to get his PR and he should not have to do that again, according to the 2004 Directive Article 16.
If I've made any mistakes in this, I am sure some of the others will correct me ( Thanks for the corrections.)