The spiderbot is the first boss of Neon Chrome, appearing on level 4 (pink rhombus).
Entering the Immersion Chair, enter the first section of the world labelled "1".
Survive the first 3 levels, or 3 levels and a special level, reaching level 4 of 30 in section 1 of 6.
Loot what you can, but keep an eye out for special stations for Perks and Weapons.
Proceed as normal in level 4 until you locate the spiderbot.
In the room with the spiderbot, there are also 3 spider dispensers. Can destroy them all to eliminate hassle, or leave 1 to build special charge.
The spiderbot has 3 forms and will switch after taking enough damage. At the start of each form will be a burst of shots, and within each form the bot fires in spurts and reloads. Try to maximize damage when it is reloading, and then avoid taking damage while it is shooting. It explodes when it dies, so take care.
Here is a video if struggling: