A lot of information is available publicly from Apple's website, at https://www.apple.com/business/docs/iOS_Security_Guide.pdf .
There are several ways how one might access the data on this phone, at least in theory.
Each file on the device is protected unless open by SHA-256 used as the hashing function. If you can crack SHA-256 at a reasonable cost, problem solved. I very much doubt it is possible. I very, very, very much doubt that we would hear about it if it is possible. It is 99.9999% certain that the FBI isn't going to crack the phone this way. It is 100% certain that we will never hear that it is cracked that way. Anyway, Apple cannot help with this.
Part of the encryption process is a 256 bit key built into the CPU. The CPU can encrypt or decrypt data with that key, but it will not reveal the key itself. If that key was known then decrypting the phone would be very simple. In that case you could make a copy of the flash drive, copy it to a supercomputer, and try all possible passcodes. But the key isn't revealed by the CPU, and Apple doesn't record the keys and possibly never knows them. BUT the key is somewhere in the CPU. It might, or it might not, be possible to cut the CPU open and search for the key under the microscope. This is very difficult and expensive. It will destroy the phone, so if it doesn't work, all is lost. There is a 256 bit key. If you don't get all 256 bits that makes the decryption job a lot lot harder. I don't know if it's possible. It would depend on exactly how the CPU is built. If possible, it would mean Apple's help is not needed. Apple cannot help with that.
There was a comment that "the NSA can do difficult and expensive". Yes, they can. I don't know how difficult it would be to extract the key from the CPU. But also, if the NSA can do it, they will want to keep this very secret. They would only use this to handle some really important case. In this case, the victims are dead, the killer is dead, there is quite possibly nothing interesting on this phone at all. The NSA wouldn't make their capabilities public for this. Maybe secretly if Apple can't be ordered to help.
Without these methods, the only way to unlock the phone is to give it the right passcode. But the user set up the phone so that its contents is erased after 10 incorrect attempts. It has been reported that the FBI did 8 attempts and they failed, so they have one free attempt and one that erases the phone if it fails.
The only way to get around this is to change the software that controls the passcode checking and the erasing; that software is called firmware. To write the software, and to make it work reliably so it doesn't cause damage, requires lots of knowledge about the iPhone hardware, so I would assume that only Apple engineers and only very few of them would have the know how needed to do this (it's not a matter of cleverness, but experience with the hardware. These engineers would find it very hard to say write firmware for a Samsung phone without help from Samsung). So there Apple's help is needed; that problem could be overcome by offering huge amounts of money to these engineers. But the other problem is that an iPhone doesn't just accept any firmware, it has to be signed with a key that Apple keeps very, very secret (because if it was in the open, the iPhone would be open to any hackers). That definitely needs Apple's help. Or breaking into Apple's computers and stealing the firmwire signing key.
Note that nobody knows definitely that Apple can create this software and install it on a locked phone. A locked phone might not accept new firmware.
A totally different method, often used, is to forget about cracking the phone, and figuring out how to get data out of the phone without unlocking it. If a user has set up their phone to backup to iCloud (which most users have) then the phone will backup even when it is locked. All you need is put the phone in the range of a WiFi network that it knows. Once the backup is made, Apple can deliver the backup to law enforcement, and that is done something they have done in the past (that would be "help by Apple", but it's "help by Apple that Apple will give without complaining"). Unfortunately someone changed that user's iCloud password, allegedly ordered to do so by the FBI, and now the phone doesn't know the correct password anymore and cannot backup. Nobody knows the old iCloud password so it cannot be changed back. Nobody knows if this trick would have worked, but since the password was changed, it cannot work anymore.
A different method has been suggested: It might be possible to examine the glass on the phone, and if the same passcode was used a lot, one might be able to determine the digits of the passcode. Knowing the digits, there are 24 combinations only. Since they had 10 attempts to try the passcode, they could use 8 attempts for a 33% chance of unlocking the phone, if the four digits were right. Or gathering all kinds of information about the person and finding significant numbers and trying eight of them. The FBI might find my passcode if they had to.
Other methods: Anything I can't think off. However, I don't see any evidence for Snowden's fifth claim.