This is by far the most difficult trophy in the game and is extremely difficult.
There are reports that you can glitch the game in such a way that you end up off the map so the zombies can't reach you but there is little to no information on how to make it happen consistently. I will detail here what I have been told but note that I have no proof that this works so take it with a grain of salt. If you're not interested in spending time trying to get a glitch to work, skip the next paragraph.
It is apparently possible to wiggle the while getting hit in just the right way by zombies at certain spots of the map. At the top left and top right of the map there is some rubble which you can edge your way into, making it relatively safe to group up zombies as they will have to funnel in towards you and can't really get close enough for more than one to hit you at a time (see Pacifist to see such a spot in action). It has been said that under just the right circumstances, you can get glitched through the rubble and end up far enough off the map that most zombies can't reach you. The only zombie that can reach you in this position is the poisonous zombie Rhino boss. The only way in this position to not get killed by the poisonous Rhino is to take advantage of Twitch keywords while broadcasting. If you can get this to work, then it would make the trophy very easy.
The following guide is based on playing solo, offline (not broadcasting to Twitch). If you broadcast to Twitch, the game changes drastically. Check the guide below (look for the red) for more info on Twitch broadcasting gameplay.
If you plan to do this legitimately (as I would suggest), you need to be prepared for the long haul. Before you can realistically attempt this trophy, you will need to have unlocked some decent weaponry. The ideal weapon to start with is the Volcano (this will be explained later), which will require that you've at least survived for 35 minutes previously.
The majority of the game can be somewhat cheated by taking advantage of the terrain. Check out the video for Pacifist for the spot you will be getting friendly with. If you're having trouble unlocking weapons, since they are all time based you can stay in the "safe" spot until the weapon you need has been unlocked (the game will give you a message saying that a weapon has unlocked). You won't be able to do an entire 60 minute playthrough in this spot, as the game spams boss monsters starting at the 45 minute mark, and they will inevitable approach and kill you if you stand there. That said, the 45 minute mark is plenty long enough to unlock all of the weapons, making it worth the 45 minutes to save yourself some hassle.
Once you have all of the weapons unlocked, start up a game with the Volcano. The reason you want to use the Volcano and not the Pepyaka Gun is that the Pepyaka Gun is best suited for large groups of weaker enemies, while the Volcano can take down bosses and, more importantly UFOs, very quickly. One of the best kept secrets about the game is that you can get the Plasmagun permanently (until the end of the current run) by destroying a UFO. The Plasmagun is arguably the best weapon in the game (save for the Spreader).
For the first ten minutes I suggest that you play normally, levelling up as you go. You want to aim to get quick reload (reload faster), burning phoenix (revive when you die), and shoot faster powerups. If you can get those early on, you can save the rest of your level ups for later in the game when stuff like temporary invincibility and kill all zombies on the map will come in much more handy. While levelling up and going for the aforementioned powerups, when they don't appear you want to focus on taking long-term positive powers while avoiding positive temporary ones (such as temporary invincibility) to save those for later.
After the 10 minute mark you will have your first boss encounter. You have a rare chance that no boss will appear and the game will tell you that "Your boss is in another castle". If this happens, then carry on as usual. If you get a boss then it will be Dongerino, the giant zombie boss with cement hands. This boss can be extremely deadly if you're not careful. Dongerino will only attack when you are in close proximity and when he does, he will smash the ground causing waves. and If you get caught in the waves you will die instantly. Also, he has a chance of turning about 75% of the hexagons on the ground red, and after he hits the ground while they are red they will all rise, killing you instantly if you are caught on one; be ready to get off any red hexagons as quickly as possible if this happens. The best approach to this boss is to stay at the edge of the map to the left, as there are no hexagons on the edges for him to smash. You need to force him to smash the ground by approaching him, as he is most vulnerable just after he attacks. Run towards him until he winds up his attack, then back off while shooting at him; you should see him reel from this. If you have the Volcano, he will go down very quickly and you can get on with the game.
After the first boss fight, you need to focus on getting the Plasmagun (if it's not already showed up). Stay in the center area of the map and hope for a UFO to show up sooner than later. Once you get a UFO try your best to focus on damaging it until it's destroyed so you can replace your current weapon with the Plasmagun. With the Plasmagun equipped, you are ready for the boring part. Head over to the area you used for the Pacifist trophy and shoot enemies as they approach. If you shoot them rather than using melee, you should kill them quickly enough to still gain levels, rather than grouping too many up all at once. You should be able to stay here until the 45 minute mark, or until another boss appears (the second boss will be a rhino if one does appear).
If you get a rhino boss, your best approach to the boss will be to play like you are bull fighting. He will constantly charge at you, and you must dodge his attacks. His most vulnerable parts are on his back and sides so take advantage of that whenever he's slowed down from charging at you. Under no circumstances should you get close to this boss, because he has an instant attack that lowers hexagons on both of his sides which means instant death for you. Just keep playing toreador with him and he'll go down soon enough.
When you've made it to 45 minutes, the real game begins so to speak. The game will start to spawn multiple bosses as though they were normal enemies, both Dongerinos and Rhinos. Dongerinos are slow moving and so are best avoided. Rhinos on the other hard are very fast moving and will be extremely difficult to avoid. The best method that I have found for surviving this final phase is to run along the edge of the arena in a big circle. As long as you are at the edge of the arena, the Rhino's attacks should miss you and you should take minimal damage from the missed attacks. You may need to jump into the center of the arena on occasion to get health drops, but I highly suggest avoiding this until necessary (I'd say at around 50% of a health bar remaining). The main reason I suggest against going into the center is that at any point in the last 15 minutes of a 60 minute run, you may get an actual boss screen, which causes hexes to raise around you, causing you to be stuck in the area until the game lets you out, which takes about 5 seconds. This 5 seconds is plenty of time for a Dongerino to approach and ground smash you into a frustratingly inescapable death, which is very painful to have happen after spending almost an hour on the game.
Keep focussed above all else, and keep circling around the arena, and after 60 minutes have passed you will be awarded with the trophy.
The following information pertains solely to Twitch Broadcasting. If you broadcast to Twitch, then the game will behave differently. If you don't have friends voting for things and entering keywords on your behalf this is not worth using at all, as the game will force you into unwanted "rewards" every few minutes, which can significantly hamper your ability to play properly. That said, if you do have friends who can help you out then this can make things a decent bit easier.
During broadcasting to Twitch, the game will give viewers options to vote on, which will appear at the top of the screen. There will be two perks to choose from, and typically one will be better than the other. The idea of this "mode" is that viewers can either help you or troll you. If you have some competent friends to help you out, make sure they are familiar with the codes on the wiki here so they can enter them when you ask them to. Do be aware that there is a 30 or so second delay on Twitch streaming so viewers really aren't able to react to the situation at hand, without you giving them orders either in person or over some chat as the delay is simply too much for it to be useful without you guiding them.
If you have a look through the above commands, you will see that there are definitely some helpful ones. It is possible to create a secondary Twitch account yourself to vote on things to make things easier for yourself. The best thing you could do in this case is to give yourself all of the positive permanent perks right at the start of the game and use other temporary ones when needed.