Joachim scored once and set up the other two to condemn the Dons to their fifth successive defeat, which leaves them with little hope of First Division survival.
Bjarni Gudjonsson and Joachim combined on seven minutes to carve open the Wimbledon defence, only for the latter to slice over the bar from two yards.
However a minute later the pair teamed up again only this time Joachim diverted Gudjonsson's through ball past Steve Banks with a firm header.
The home side lacked spark and were resigned to hopeful shots from long range as they struggled to get a hold on the game. Nick McCoy tried his luck from distance and Nico Herzig made several attempts to unsettle the Coventry defence.
Joachim should have added a second after 27 minutes after Wimbledon failed to deal with a corner. And 13 minutes later the visitors doubled their lead through Patrick Suffo.
Joachim's jinking run ended with the ball at the feet of striker Suffo and despite a desperate attempt from Dean Lewington and Ben Chorley the ball found it's way into the net.
Gudjonsson and Joachim were proving too difficult to deal with for the Dons and on 63 minutes Joachim turned provider again to tee up the midfielder.
Gudjonsson took his time and drilled a right footed shot past Banks.
On 76 minutes Darlington chipped in but Dean Holdsworth failed to get the vital touch on the ball.
Holdsworth tried his luck again two minutes later with a first-time effort from Banks' long kick but his volley drifted wide.
In the dying minutes Wimbledon had their best chance of the game as the ball fell in the six-yard box. But as Peter Clarke fell on the ball Lewington took out his frustration and received his marching orders.
Wimbledon: Banks, Darlington, Lewington, Herzig, Gier, Campbell-Ryce, Hawkins, Chorley, McKoy, Small, Mackie.
Subs: Holdsworth, Gray, Gordon, Kamara, Worgan.
Coventry: Shearer, Deloumeaux, Konjic, Clarke, Grainger, Gudjonsson, Doyle, Safri, Warnock, Joachim, Suffo.
Subs: Shaw, Pead, Barrett, Ward, McSheffrey.
Referee: S Tanner (Bristol)