At 100% strength magnification, Elizabeth has 60,000 health and deals 250 damage per hit. She also creates a Level 3 Shockwave per hit. She has a range of 170, with area attack.
Elizabeth has high health (Even more with the 700% boost) but relatively low damage and range. However, she has 100% chance for a Lv. 3 Shockwave, meaning that any meatshields are pretty much worthless: To beat her, use only strong, high-health troops, such as Mythical Titan Cat.
Strategy 2 (QUITE DIFFICULT)
If you have a high health base (80.000+) (mine 104.000) just spam Paris cat (lvl>20, mine 25+1). At first upgrade the worker cat and send 1 Paris to kill the peons. When elizabeth comes out start spamming Paris and it's Done. Elizabeth will hit your base but you still will win (104.000 to 40.000 health)
Scion of the cyber-pigpen, Liz almost ended her line after choking on a mushroom. She's still blue to this day. Uses powerful wave attacks.