Spider Physiology: Thanks to the events of Spider Island Anya possesses some off-shoot copy of Spider-Man's powers, granted to her by the Jackal's machine. The radioactive spider bite was in essence recreated in her, the complex mutagenic enzymes in spider-man's blood were transferred triggering numerous body-wide mutagenic changes within, granting her superhuman strength, speed, toughened flesh, and possibly numerous unknown arachnid-like abilities.

Superhuman Strength: Anya's strength is relatively large at her stage in heroism. Her strength may also be increasing, because she was quickly able to subdue Arachne, who can lift 10 tons. however, following the events of Spider Island, her strength has increased to a level comparable to Spider-Man's, if slightly less.
Superhuman Speed: Anya can run and move at speeds that are beyond the physical limits of the finest human athlete. She is ultimately capable of running at speeds in excess of 30 miles per hour.
Superhuman Stamina: Anya's advanced musculature produces less fatigue toxins during physical activity than an ordinary human. This allows her to exert himself physically for much longer periods of time before fatigue begins to impair her.
Superhuman Agility: Anya's agility, balance, and bodily coordination are all enhanced to levels that are beyond the natural physical limits of the finest human athlete. Araña is extraordinarily limber and her tendons and connective tissues are twice as elastic as the average human being's, despite their enhanced strength.
Superhuman Reflexes: Anya's reflexes are similarly enhanced and are currently about 10 times greater than those of an ordinary human.
Wall-Crawling: She has the ability to cling to walls at will.
Biological/Organic Webbing Generation: She has the ability to organically produce her own silk webbing from glands within her forearms, limited by her body's health and nutrition. These organic webs has many of the same properties as Spider-Man's artificial webbing. The silk is released through a spinneret near each wrist containing a central web spigot orifice used for web-slinging and drag lines, supplemented by several radial minor spigots for other types of webs connected to specialized glands.
Shadow Camouflage: She is able to hide in shadows and go completely undetected by most people. Whether this is an actual power or simply stealth remains to be seen.