Okay, this isn't going to be too comprehensive, since, as a roguelike, I can't provide guides to the specific levels, just general tips about how I grabbed this in a ~3 hour playthrough.
1 - Don't be quick to leave the slums. Your job at the start is not to make a lot of money, but to get your multiplier as high as possible by grabbing 80+ percent of the loot. Getting all of it offers a nice cash bonus, but is not necessary, since right now you just want to focus on getting 8 successful heists, pushing your multiplier to 2.6. This shouldn't be too much of a challenge with just hacking 1 and double jump. Once you've got 5000 buy bombs, which should help you deal with the security cameras that start appearing once you've got around 5 successful heists. Just bomb the ceiling above the security camera, and problem solved. Make sure you don't buy higher security clearances yet - you only get experience level boosts on your highest security level runs - so you can't move on to warehouses and then come back and farm the slums.
2 - Once you've got over 9000 pounds and a multiplier well over 2, buy the warehouse security access and hacking level 2. I hope you like the warehouse level, because this is where you'll be spending most of the game. Focus on breaking in, hacking a computer or two, and then getting out - if your multiplier goes up, great, but it's not what you should be focusing on. Just keep replaying the level, using bombs to destroy pesky security cameras so you don't have to worry about hacking speed. Once you've got the 25K, buy a BUG, and start using it on each new trip to the warehouses.
3 - Now that unlimited money is rolling in, buy the melee power-up - this allows you to 1-hit basic drones and hug robots, which are your biggest danger at the moment because of their unpredictable movement. Also remember that bombs can destroy blade caterpillers, which is always a good idea, since it's way too easy to forget where their corpses are. From here it's just a matter of replaying the warehouse over and over again, planting bugs and letting your bank account swell. The best part about the Warehouses is that they're so short that you'll rarely be there long enough for your bugs to be found - it's not too difficult to get around 1000 pounds per second in income.
4 - You can upgrade things in any order you want, whatever best suits your playstyle - I grabbed wallhang and extra bombs, but everything will make the game easier at this point. Once you've got steam purge and remote detonate you should be getting multiplier bumps almost every trip through the warehouses. Once your multiplier is over 4 you should have most of your abilities unlocked. Make sure you've bought noise goggles and stealth, then proceed to New Belgravia.
5 - From here on out the game should be a breeze. With everything unlocked you should be able to play the game as carefully and slowly as you want - more importantly, you don't need to worry about 80+ clearance rate on any of these areas. If you do it, great, but with a multiplier closing in on 5 and 2 bugs on every level, whether you complete things or not you should quickly find yourself with enough cash to unlock all of the security clearances before you even get to 60 days left.
6 - Tips for the Basilisk: with a fully-upgraded thief this isn't very difficult, the one thing I'd advise is that you locate the basilisk as early as possible and make sure there's a clear path from it to the exit. Don't be afraid to bomb the hell out of the levels in order to make that path a reality. Ideally you should be able to run from the Basilisk to your pod in under ten seconds. If your basilisk doesn't spawn conveniently - for example it's far underground - don't be afraid to just run back to your pod and try again. Yes, it's 400K each attempt, but at this point one trip to the banks should earn you that.
Beyond that, it's down to skill and patience, so good luck!