This isnt going to be a full depth play by play guide but more of a the basics of making this as painless as possible. Remember to be on iron man as well.
Let me clarify one thing about the achievement before we start. Despite it saying "Starting as an Iberian Christian, convert all of Iberia to Christianity" there is a little more to it. You need to control ALL of Spain, have it be Christian, AND you need to control the duchy of Barcelona despite it being de jure to france. Just to state the obvious, Christian heresies do not count as Christian.
I went for this on my first playthrough because i loved playing as spain in CK2 so i naturally just went for it. I started as King alfonso in 867 and before anything happened I married the king of france's daughter. You are very weak in the beginning so having france as a ally helps a lot. As you play through and conquer hopefully your prison will be filling up with those filthy muslims infidels! An easy way to quickly convert counties is by negotiate release with muslims prisoners and making them join your court and gaining a weak favor on them. Then give that muslim a muslim controlled county and use that weak favor on them to convert to Christian. When they convert to Christianity they will will convert the county with them.
I personally get religious icon (in the theology tree on the lefthand side) skill point on every ruler as fast as possible. It really cuts down the time it takes to convert counties. Lastly, if you get a bad bishop with a terrible learning skill it may be worth to assassinate him because having a bishop with a poor learning skill can drastically increase the time to convert counties.
Heresies are a huge pain in the ass because when vassals join a heresy they convert the county to that heresy as well. To deal with this we can do almost the same thing to the muslim prisoners. Demand them to convert and if they refuse you can imprison them. After 5 years you can tell the imprisoned vassal to convert and they will be release, convert back to Christianity, and convert the county. If you have the money and if you want you can pay for them to come back to the faith or if you dont want to pay you can still imprison them and wait 5 years for them to convert. When you fail to imprison a non-direct vassal there is a chance that the game will slightly bug out because they will revolt and then the revolt will end. I do not know why this happens but you can sway these vassals so they like you more and will be more willing to convert 5 years down the line. Another thing to note if a vassal holds 2 counties and they convert to a heresy they will convert the 2 counties they own as well. When you demand conversion and convert them back only their primary county convert backs meaning that 2nd, 3rd, or how many counties they own will still be a heresy. So keep that in mind.
This is my very first guide and I do not claim to be a expert in any way shape or form. I started in 867 and got the achievement in 1020. If there are any suggestions on how to make this guide better please add it to the comment and good luck on your achievement!