I doubt I'll ever beat it without healing...I may be able to do it with 1 (the First aid spray the game starts you with) because of the snake (though I imagine I could avoid damage from the snake altogether only it would take longer than healing would; anyway I can't say for sure).
I had a sub 1:11:30 run going until I died at the Tyrant.:-( I'm going to give him a good hour or two practice over the next 5 days to make sure it won't happen again.
I now believe a sub 1:10 run may be done by me and that the best time possible could be around 1:08-1:09.
I had my 2nd game in a row ruined last night from the fight with Tyrant...the worst part is that the night before I practiced the Tyrant fight and beat him 15 times in a row without having the heal.
Fortunately I have checkpoints listed for various games so I was able to accurately judge what my final time would have been if I was able to beat Tyrant...the run would have been approximately 1hr 10min and 13sec. I know I'm going to get a sub 1:10 online though I'm not sure how much more time I'll be able to take off. I'm expecting my final run will be a 1:09:xx.
I've finished the game in a time of 1 hour 9 minutes and 17 seconds; healed 4 times which sucked but I did end with a no damage Tyrant fight. I imagine I can beat the game in under 1:08:30 (maybe under 1:08) but this may be the run I submit to the site as I'm getting tired of playing this game (though I can always work to improve it a few months later). I suspect that 1:07:00 is around as good as it gets (maybe not even that low).