Weed killer?

I find brute force works best for me. Just grab it by the crown and yank it out. It snaps off easily. A spade will slice though the main stem or a knife should take care of it. It's all gone in the blink of an eye.

As Bathgate says, they have a simple tap root, and an ordinary "snake's tongue" weeder does for them easily.

As above, pull them up. If you really think that the aquilegias spoil your garden then dead-head the ones you keep to prevent them seeding.

Wish we had only a hundred! I have pulled out more than that over the last few days just doing the lawn edges and weeding the first foot of the borders as I went along.
Wish pulling them out worked. Here it seems that any bit of root left in re-grows, like dandelions do.

Hmm...never had that happen with me, but Aquilegias are medium difficult in my area.

Annoyingly the only one which does not seed all over the place is A. ottonis which is a tiny blue and white species.