House of Blossoms is going to be the easiest map to get this. I have included a video for getting 8 million points on this map, without being spotted, taking no damage, reaching the exit, and finding 174/176 loot. - credit for this video belongs to HolyWarr27
-People have commented that they too have hit around 8 million by following this video!
The majority of your points come from picking up loot in 1 long chain. From the time you pick up one item you have 60 sec to get another, some guards have items to grab too that count. If you grab an item in under 10 seconds from the previous one you get a bonus, based on the multiplier, so try to go fast.
The normal loot item locations do not change so be sure to remember where you find them for future playthroughs.
When picking a lock use focus to slow time down. When you you enter a room try to grab all items out in the open first before trying to pick a lock or open a frame - these two things will more than likely burn up more than 10 seconds causing you to lose out on the quick pick bonus.
Guards - each guard has a patrol pattern, learn them! Some stay to a specific room, others wander the halls. Avoid being spotted - an open confrontation takes more time to deal with and also can cause more points to be lost. Be sure to distract guards if you want to avoid them or knockout/kill them while the are by themselves.
On the Manor, all guards knocked out is - 330,000 points. House of Blossom all guards is 390,000 points.
When you knock out the guards, (Holding down RB will make the player hold on to and automatically loot the body, hit B to drop)
Lights - Try to avoid taking out lights unless it is just to distract a guard. This takes up more time than it saves in my opinion. Use swoop to traverse areas that are lit up. Alternatively distract guards patrolling the bright hallways by shooting arrows or tossing breakables behind them instead.
For the House of Blossom map you have a lot more room for error. Essentially after taking out all the guards you will only need to find about 150 loot, in 1 chain, and make it to the exit. If you cannot find 150 check out my video for locations on most of the 176 loot on the map.