Secret rifts can be spotted with R-goggles, they emit dark particles. Rifts disappear after you enter them, so you better save beforehand if you want to revisit more challenging ones. There's 3 in each world and they have points, 1-ups and rarely weapons and powers. You usually have to avoid walking under arcs or getting hit by lights.
Points counted across all missions.

World points: 54500
Quest points: 82000 (best outcome) +50000 if you bring WP-Gun to quest giver again
Rift points: 10000

Shop area entrance
On a cliff near bridge
Looter base gates

World points: 12800
Quest points: 15000 to 20000
Rift points: 17500

Right outside tower, jump (early teleport power)
Above ruins
In first area of underground

World points: 0
Rift points: 18000

Room 309, needs lost key (power)
Inbetween shelves
Near sewer grate when chased

World points: 88400
Rift points: 35800

Robot town, near elevator
Between DM-017 and DN-017, jump from tower above walkway
Behind a crate in barracks area

World points: 4500
Extra points: 100 for hitting a target (100 hits needed for power)
Rift points: 29200

Behind a tree before entering military base
Area inbetween Major boss and storage room
On top of the storage room

World points: 61000
Extra points: Colloseum tournament rewards (15000 - 30000 - 50000), Bird hunt rewards (25000 all birds, 50000 no misses)
Rift points: 42800

Corner near the bar
As you enter colosseum and games area on the left (CSG-16)
Jump above the carpet

World points: 70000
Rift points: 84600

Jump down in this area
Area with lots of climbing near 1-up
Behind some pillars near idol on the left side

World points: 48000
Rift points: 33000

Cliff leading to observatory
Area with lots of rits (Order)
Corner of the village

Book in room 4 of Teira inn gives a few hints to figure out math.
Dot = 1
Horizontal line = 7
Vertical line = 14
Square = 21

You only need to use multiplication (on the right) and division (on the left) to figure out what you need. Not sure what 2 operations in the middle mean, probably XOR.

For this puzzle you don't actually have to do any math, everything is already solved in room 4, just read the resulting numbers backwards.

Alternatively just look at this prisoner for solution.

This is a code that's used in the 9th world, you'll need to know about symbols from temples and their numbers.

Teira 49 92 45

Lesna 77 96

XE-89 51 52 14

Masitek 11 83

Suraja 23 42

Bangahar 72 39 71

Kant 89 34

Haos 16 27 63

Not required for anything, just for fun. All you need to know is which actions give you the most points.
Grab + knockout gives you 400, shooting limbs gives 20, headshot 50. Human enemies have 40 health and using low damage weapons like Dart and Trai-LV on limbs will give you a few hundred more. Some rooms can spawn more enemies if you shoot a loud gun, but they can quickly disappear after getting knocked out, enemies that were in the level originally don't despawn.
Use Trai-LV for Legion, more hits = more points, of course you can't get hit and use powers.