As noted by Michael Edenfield in his answer to a related question, the bootstrap and predestination paradoxes are very closely related. It's not unusual for a work of time travel fiction to involve both simultaneously, and this one does.
The case for a Bootstrap Paradox
The bootstrap paradox is when an object or piece of information has no "source"; a perfect example is provided on the Wikipedia page:
An old woman gives a young man a watch; the young man then goes back in time and hands the watch to a young woman; she later grows into the older woman who hands the watch to him. The watch therefore has no point of origin1.
The watch never "begins" anywhere; there's no point in its timeline where it can be manufactured or assembled. And if it's never assembled, how can it exist? This is the core of the paradox.
In Predestination, Jane's genetic code is the subject of the Bootstrap Paradox. Looking at Jane's timeline, this becomes clear:
In humans (normal humans, anyway), our genetic material comes from our parents, which comes from their parents, and so on, all the way back to Y-chromosonal Adam and Mitochondrial Eve. This is not true with Jane: because she is her own father and mother, she is also her own grandmother and grandfather, and so on. Her DNA never makes it back to Adam and Eve.
Jane's genetic code is fundamentally the same as the watch in the example above; it just goes around and around it's own timeline, with no "start".
This is exactly a Bootstrap Paradox.
The case for a Predestination Paradox
The difference between a Bootstrap and Predestination paradox is sometimes hard to wrap your head around, but Michael Edenfield does a good job in the above-linked answer, so I'm just going to quote him:
[A]n event in the past creates a chain of events that leads to some second event in the future, but that second event is ultimately the cause of the first event.
How this works is hard to explain in words, so I created a diagram. The diagram shows only a few of the events of the film, but it summarizes the closed loop I wanted to illustrate:
As you can see from the above (spoiler-hidden) diagram, the events of Jane's life form an inevitably closed loop: her existence is dependent on choices she makes after she is born, and because of the unique circumstances of her birth2, she inevitably ends up making those choices. Paradox.
It's technically possible to get around this problem by introducing multiple timelines, but this is not the case in Predestination.
The Temporal Agent renders the Predestination paradox absolute, because he remembers all of the events he's causing - the loop I described above must have happened, because otherwise the existence of the Temporal Agent (and his memories) is impossible.
1 I'm ignoring the complication that the watch would get progressively older and older each time it passed through the loop, until it eventually broke. This issue is sidestepped when you're dealing with information, but tangible objects make better examples
2 I left those out of the diagram for brevity. The full interconnectedness of Jane's timeline is way too complicated to summarize