Please help with identify SF movie from 80's with cyborgs

I saw this movie in early 90's, but it could be from 80's. I recall few scenes:

It was set in the future or in a parallel universe. Cyborgs in black armor were the bad guys. Humans lived in the city under a dome that consisted of hexagonal tiles. One cyborg is shooting with a weapon into tiles and they are breaking apart. He was able to shoot only few before he was attacked by a good guy with a sword(?) who ripped the heart out of the cyborg and connected it to a device with monitor, whereupon a cyborg chieftain was visible. He had a black wire connected to the nose. I recall that good guy said something about "black heart".

Another scene was in our world or times. The good guy was chasing the cyborgs (or maybe they chased him through time and space?). Cyborgs were in some cave waiting to find the good guy. And he landed in place that reminds an American small town, ruled by a sheriff. A woman was helping the good guy, but he was captured by the sheriff and locked up. He had something like a watch that probably jammed cyborg detection sense so they were in stasis in mentioned cave. The sheriff took away the watch, which caused cyborgs to wake up and detect the good guy.

This is The Time Guardian (1987).

A time traveling city under attack by cyborg robots in 4039 travels back in time sending two troopers in advance to the Australian desert year 1988 to prepare for its arrival. The enemy tracks them.

This is an Australian film, presumably inspired in large part by The Terminator (1984).

The opening scenes take place on a post-apocalyptic Earth in the year 4039. A human city surrounded by a dome-shaped force field is under attack from black-armoured cyborgs called Jen-Diki. The protagonist, Ballard, is a human soldier from that time period, and after killing a Jen-Diki that was firing on the city's force field with a bazooka, he's shown to extract its "black heart" with a combat knife.

As a means of escape, the humans decide to transport the entire city back in time to the 20th century, but it moves slowly backward through time, taking a day or so to complete the journey, so Ballard and another soldier, Petra, are sent ahead to prepare for the city's arrival. They arrive in the Australian outback, not far from a small town, but are followed by the Jen-Diki, who injure Petra, rendering her inactive for much of the film. The Jen-Diki are sensitive to light, so they too spend much of the film inactive, waiting in a cave for the Sun to go down.

Meanwhile, Ballard befriends a geologist named Nikki Coghill and has a couple of run-ins with the local police, which results in him getting thrown in jail. The police sergeant confiscates a high-tech armband Ballard was wearing and starts mucking with it, which draws the attention of the Jen-Diki, who attack the police station shortly afterwards.