For those who've played the game, you'll have come across the hidden synergies- combinations of Perks and/or weapons which provide additional bonus and weapons for a player to wield against their enemies. Having recently interviewed The developer, I actually managed to get a comprehensive list of how to unlock them, though not necessarily what they do.

Let's Get This Party Started
Kill Repeater - Combo Buffs Activate Earlier.
Recipe:
Firewall
Sequence Optimizer
Death From Above

Denullifier - Pick up nullified projectiles and use them as ammo.
Recipe:
Prophet Core: Local Area Nullifier
Saving Grace
Kinetic Lance

Nuke Suit - Explosions can only do 1 damage to you.
Recipe:
Flack Jacket
M. Fission
Kwang-Grade Stompers (Runnels Ability)

Dangerous When Laserous - Energy weapons have faster firing speed.
Recipe:
Neon Chrome
Juno Core
Bandoliers

Night Terror - When teleporting from a Night weapon, nullify all nearby projectiles.
Recipe:
Tempest Core: Deep Shadows
Blood Bait
Night Machine

FMLRIZER - Faster attack speed.
Recipe:
Neon Chrome
FMLR LZR (Drone weapon) - Requires Tinker to pull it off a droid and wield it.

Living Weapon - An extra dash for the embodiment of chaos.
Recipe:
Uber Core: Ground Slam
Juno Core
Remorse Suppressor

Bullet Efficiency - Sometimes firing weapons doesn't use ammo, but energy weapons break when trying to pick them up.
Recipe:
Synaptic Trigger
Heavy Belt
Trigger Fingers

Dead Of Night - Kills grant an extra few seconds of deadlock time.
Recipe:
Night Piercer
Time Reaper
Insectivorous

Doomed Soul - Some armor, all your blood is also armor. Your blood can no longer become infected.
Recipe:
Doomed Valor
Blood Bait
Nails Implant

Sandbagger - Your starter pistol is upgraded.
Recipe:
Doomed Valor
Time Reaper
Survivor's Pistol

Vantasm - All weapons fire faster, but your blood is now infected.
Recipe:
Black Mirror
Blood Bait
Blak Rifle

Jr. Anarchist - Become immune to fire.
Recipe:
Synaptic Trigger
Snake Bite (Hauer Starter Weapon(?))
Black Richter

Gemini - Two great tastes that taste great together deserve an extra dash charge.
Recipe:
Synaptic Trigger
Null Mass Cannon
Lil' Brother

Skyvader - You've combined your weapons into the Skyvader. (A useful weapon that is powerful, and fires a beam that cancels out projectiles).
Recipe:
Synaptic Trigger
Black Richter
Electron Pistol

Needle Threader - Dashing through bullets will heal you for even more.
Recipe:
Saving Grace
Heavy Night Nail

Blak Threader - Your deadlock time ticks down faster, but dashing through bullets will earn you back time.
Recipe:
Melt Core
Blak Nail

Night Piercer Set - You've modified your night nail into a stronger weapon.
Recipe:
Night Piercer
Night Nail

Sharper Boots - Fast dropping can now slice projectiles that are underfoot.
Recipe:
Heavy Boots (Hauer Ability) OR Crat.R
Nails Implant
Night Piercer

True Believer - Slice nearby enemy projectiles whenever you're teleported.
Recipe:
Night Piercer (The modified weapon)
Night Nail

Faith Healer - Regain more time from Overstimulator Perk.
Recipe:
Grim Determination
Overstimulator
Black Richter

Heavy Needler Set - You've modified your Needler into a stronger weapon.
Recipe:
Nails Implant
Needler (Sioux Starter Weapon)

Unofficial Synergys
Whilst there aren't Many in this regard, it should be noted that The melt core provides you unlimited dashes- which is amazing in itself, but truly shines in conjunction with any of the mass cannons.

The reason for this is because they use dash charges as ammo, allowing you to spam their highly damaging AOE hits as quickly as you can fire the weapon, allowing you a -very- different way of progressing forward through the game.