SpiderHeck

Similar to the Wave 70 achievement in the base game, there's a LOT of luck and a lot of skill that goes into completing this, more often than not you'll be forced into playing on horrible maps and most runs you'll be lucky to see a single good perk. It's also worth noting that only the Pain Level 1 achievement seems to unlock in co-op, this one needs to be done solo. They can all now be unlocked in co-op!

First off, here's all the modifiers for Pain level 7:
Objectification Perk - Allows you to attach your web to enemies.
Dangerous Enemies can appear straight away, more enemies will spawn.
Waves per map increased from 3 to 5, Perks to choose from reduced from 3 to 2.
Increased spawn chance of basic particle blades.
All weapons only get one shot, Particle blades break after one hit.
Max Lives reduced to 1.

Perks

As you can see it's no joke, you really have to get lucky with some useful perks, maps and spawns or have a god run to get through this, here are the best perks to look out for:

Safety Net - Gain a shield on last life - Since we only have 1 life we get this shield at the start of every map, This saved me 3 times in my successful run (I got very lucky), it's not guaranteed to save you but when it does it's huge and basically an extra life without resetting the wave.
Efficiency - Weapons have more ammo - Most weapons get an extra shot and Particle blades can take one extra hit before breaking.
Spider Storage - Max lives increased - Increases max lives by 1, you don't get this extra life after taking the perk you still have to earn it by surviving the next 5 waves. But again an extra chance is huge when you would normally only have 1 life.
Picky - Choose from more cards - Best picked early on in the run but this is just to improve your chances of finding one of the above perks or a decent map to pick later on.
More Guns - Guns spawn more often - Since blades break after 1 hit, guns usually become the best option for quickly deleting enemies, this ones more a preference thing though, if you find you have better luck with the blades you can ignore this.

Some other decent ones: Size Matters - Particle Blades are longer, Thick Blades - Particle Blades are wider, Fatigue - Enemies move slower, Portal Interference - Slower enemy spawn rate, Feeble Enemies - Enemies suffer more knockback, Particle Technology - Particle blades cause more knockback, Insulation - Briefly survive the death zone, Selective Blindness - Enemies are less afraid of the death zone.

Maps

So for the first 10-15 waves I would generally prioritise picking good perks no matter what map they appeared on, but after that you 100% want to only pick good maps wherever possible, any big maps with lots of open space and a route to path enemies around are a good pick, anything small, enclosed or with lots of moving parts, and especially anything with portals is a really, really bad pick. Here are, in my opinion the best and worst maps to pick later on in your run:

Best Maps: Core, Hecksagon, Big Wheel, Space Rocks, Shuffle, Burial, Balance, Polaris.
Mid Tier Maps: Smash, Fungi, Ribs, Tick-Tac, Humdrum, Swings, Ant Domain.
Worst Maps: Upside Down, Rocky Loops, Pachinko, Dead Weight, Trash Barrage, Cove, Arachnobatics, Cargo, Tribune, Hanging, Launch, Skull, Bouncer, Dagobert, The Bigger Spinner.

General Strategy

Ok so you know which perks and maps to look for, now for the actual run. First off learning to throw and pull back the particle blades is huge as they will be spawning everywhere and a well placed throw can delete enemies without putting yourself at too much risk, you can also spawn kill enemies safely with a well timed throw. It's mostly a case of picking blades up and throwing them until something hits, try to keep one handy for defence when going against the dual blade flies but ideally you'll never get close enough for them to charge at you.

Always plan your escape routes, the best maps all have a good loop around the entire map, so just pick a direction and make your way around while rotating through as many weapons as you can. Guns and explosives, while rare can be vital for getting rid of some of the more annoying enemies so make use of them whenever you can, the gravity grenade in particular is a get out of jail free card, just make sure you use it instead of having an enemy hit it towards you.. The only weapon I would actively throw off the map is the red Hecksaw, this weapon is far more dangerous for you than any enemy in the game lol. The purple Gravity Saw is also quite dangerous to use but just fire it where it won't bounce too close and you should be fine.

Ultimately just play safe, take your time and hope you get lucky with perks early on and map choices/enemy spawns in the later waves, thankfully it's only 30 waves so the runs aren't too long, just keep practicing and eventually you will get this.

My Successful Run

Safety Net - Gain a shield on last life
Power Web - Stronger web pull
Portal Interference - Slower enemy spawn rate
Immovable Object - Spiders suffer less knockback
Too Cool - Get closer to explosions without dying

Not the best perks but starting off with Safety Net really made my run possible here, Power Web made Space Rocks a very difficult map to play on and the rest of my perks had very little impact on the run, although slower enemy spawns is a nice one to have. Ending on the Big Wheel map really helped as there's a lot of places to funnel enemies in and escape.

Spiderheck - Pain Level 7 Wave 32 - Full Run