Alpacky is a buffed Alien Camelle with a much slower attack rate. She can survive a lethal strike, and when her health reaches 1%, her damage increases by 900%. In other words, when Alpacky survives a lethal strike (or slightly before), her damage multiplies by 10. Save a damage-dealing Cat Cannon for her lethal strike, use units with longer range than her, or with good timing, fast units will attack her before she can attack them.
Li'l NyandamCAN be a non-Uber alternative. Albeit very inconsistent, as even though he outranges Alpacky in stat terms, within the game, this may not be the case, see this video to see an explanation.
If you have no units that outrange her, use tanky melee units like Jamiera/Crazed M. Titan. Save your Cat Cannon for when she survives the lethal strike. By then, her ability will have activated, and she can deal extreme damage. Use your Cat Cannon to finish her off. However, if you are unlucky, the ability will activate before the lethal strike. If that happens, use units with good speed like Crazed Cow, Maglev Cat or even Valkyrie Cat.