I've calibrated my axes, levelled the bed, and I've calibrated my extruder steps per mm, but I'm really struggling to print parts with fine details. I'm trying to print these chain cable links, but one of the finer parts keeps lifting from the bed:

Those little "spurs" are 2mmx4mm, and in later layers the lift from the bed is enough to cause the nozzle to dislodge the print from the bed (the links in the background were printed before I started properly calibrating my extruder btw). To aid with bed adhesion I tried printing with a brim, but now I'm getting this problem:
The brim appears to be lifting from the bed and getting totally messed up.
What's going wrong here, and where do I need to look to fix it? Is this still an over-extrusion problem? I can post my Slic3r & firmware settings if it helps.