Formalities after Maltese citizenship by descent

Sorry it's a bit of a long reply hope it helps.
You don't mention if you were born in Malta or not, let's assume not.
You will also need to fill in the passport application form, on this form also states that you will require a photo that has been authenticated by someone that has known you for at least 2 years, see application form, and they will check, you will need a Maltese person to do this if living in Malta, your citizen certificate and/or letter that denotes you have duel nationally. ( including one born in Malta ) There are two prices for your passport and that depends on when you apply for it.
Also make sure when registering your birth that you fill in the correct form, one for those born in Malta and one for those not. Registering your birth will cost you €2.60 then either €2.60 each for a “short” birth certificate or €9.60 each for the full one. When registering you will need your application form, your certificate of nationality, and your certificate of birth. All original copies which they keep. Your birth certificate will take about two weeks to process, then you can apply for your passport once your in possession of all items. If you know anyone in Malta they can register for you as long as they have the correct items.
I would look at the IDMalta website to download any forms that you require, read carefully although the site can be in English it's geared up for natives, take as much evidence with you when you apply, ie grandparents birth certificates, gt grandparents certs.
Unlike in the U.K. once you have one government ID eg driving licence/passport they don't share with the other departments.
Don't expect to come over for a couple of weekdays and get everything done it won't happen.
I'm living here in Malta since Nov'20 and I'm still having problems.
One last thing, if you come over to do this, be careful of the address on any paperwork as the office has just moved from Valletta to Marsa. Check website. https://identitymalta.com look under Units.
Good luck.