1.) Make sure to have multiple types of damage. For the purposes of making things efficient, archgun is preferably Radiation. The rest of your weapons (Primary, Secondary, Melee) must embody the other elements, usually having IPS + 2 elements, one combined (Corrosive, Viral, Magnetic, etc.), one base (Fire, toxin, etc.) Weapons like Zenith will help, as the infinite punch through will help against the pylons.
2.) Bring a warframe like Chroma. The fight will almost always include getting hit multiple times, hit by multiple enemies, chroma taking advantage of that. So, keep moving, and shoot the spider with the appropriate gun you modded it for.
3.) Make sure you have your archgun well modded out. Imperator vandal and Corvas are popular options to deal with the limbs easily.
4.) Be aware of the phases. Shields down = get archgun out and shoot the legs. Otherwise, watch what element the spider is currently vulnerable against, labelled on the face of the spider. Using your operator amp to shoot switches the element, which will help if you do not have that damage type.
5.) There will be 4 phases to the health bar, each with 3 mechanics in different order. One will be shooting its shield down, one is shooting the limbs and one is shooting the pylons. You will need to shoot the limbs 4 times, the last being under a 5 minute time-attack.