First of all, congratulations on the first win!
Going after Heavies is indeed quite dangerous, usually best avoided if at all possible unless you have an ace up your sleeve (of which there are many, of course, but still, Heavies can be big pain points, especially in Research anyway).
Once you hit high security you'd better have an exit already pinpointed, or a build ready to face even high sec head on
![Smiley :)](http://www.gridsagegames.com/forums/Smileys/default/smiley.gif)
I will say though, definitely no luck required once you've built up the right combat skills! It's more dangerous, to be sure, but realize that the top players can defeat high sec on every single floor and win. Plus there are extended wins which are much harder than the regular game you've been playing, and they can reliably crush those too
![Wink ;)](http://www.gridsagegames.com/forums/Smileys/default/wink.gif)
There are a bunch of videos you can check out of folks doing this sort of thing, or crazier. Actually almost all of my own runs are full combat runs and I tend to win all of them unless I'm doing something stupid on purpose (you can find them archived on my YouTube channel). Among them I also did a run where I was sterilizing every floor (killing enough bots that they eventually evacuate everyone and fry the entire floor to burn you out), but for me while streaming that's also a relatively slow style so I quit after doing that four times through Factory xD). Even more recently I had a powerful build that got stuck with higher alert in -3/Research without enough time to find an exit and ended up high seccing and went ahead and just sterilized that floor using siege mode, shields, and good EX launchers.
Regardless of build type though, the last several floors require a much different mentality to succeed, and will
really test your build and skills. To be sure, avoiding enemies that you don't gain anything from fighting is usually preferred, even with a heavy combat build, though there are also those who will show off and do stuff like lyrabold's recent run (at the top of the Beta 13 leaderboards right now) where they intentionally sterilized every floor, and continued clearing entire floors
even into the extended game, killing all bosses and destroying a total of 11,865 robots
![Tongue :P](http://www.gridsagegames.com/forums/Smileys/default/tongue.gif)
If you're interested in learning the ways of combat, I recommend checking out some videos or (perhaps more easily) visiting the spoiler channels on the Discord server, as that's where all the top players hang out and are happy to offer advice.