Well, for more bloodbath we can't have one side obtaining a decisive victory early on, so early attacks on British carriers would need to be averted. Let's see:
Argentina occupies the islands with mountain troops led by a competent commander. ARA General Belgrano and one of the Argentine Type 42 destroyers are intentionally run aground in port at Stanley, to cover the area with their artillery and missiles.
The runway at Stanley is prolonged, Mirage III fighter-bombers are deployed there and used to attack the British fleet and engage Harriers in air to air combat.
The Argentine garrison at Georgia is larger and resists. It's eventually beaten, but an amphibious attack in near Antarctic conditions would take a toll on the British.
British submarines sink the Argentine carrier ARA 25 de Mayo before the (rest) of the Argentine surface fleet pulls back to port (ARA General Belgrano is at Stanley in this scenario)
One of the British troop transports gets bombed at San Carlos. The bombs detonate.
Operation Mikado goes ahead. Operation Algeciras goes ahead too, sinking a British tanker at Gibraltar.
The small argentine force covering the site of the landings at San Carlos has working flares, manages to illuminate the disembarking British troops and fire on them accurately with recoilless 105mm guns. They are eventually defeated, but manage to inflict casualties on the British.
Argentina fixes the issues with the submarines torpedoes before the war. While Argentine diesel subs can't get in a position to attack the British carriers (if they both get mission killed, it either ends the war or postpones it to the next year, so we don't have that much of a bloodbath), they get to engage and sink British ships later on the war. Or:
This one is tricky because it requires several days of bad weather, ideally across most of the theater and for Argentina to know where to find British ships. The Battle of San Carlos would provide the best combination of the above, but prolonged bad weather may as well delay the landings instead. In any case, the Argentine missile corvettes sortie from port, taking advantage of cloud cover to delay the time satellite reconnaissance would show them away from port and the reduced sonar performance of the British subs due the storms above. Bad weather may also impede attacks by British Harriers or the Argentine task force may be given some degree of air cover from Stanley based Mirage IIIs. Bonus points if Argentine diesel subs are waiting for the corvettes near their target (any significant group of British ships). Argentine and British surface ships and submarines engage in a modern sea battle. None of the Argentine corvettes survive the encounter but they manage to take a toll on the British surface fleet.
British troops eventually reach the Argentine lines but facing better trained troops (and maybe with better air cover) have a harder time breaking through the Argentine defenses. Eventually the hills west of Stanley are taken by the British but the remaining Argentine garrison still resist in Stanley and house to house combat ensues. Bonus points if ARA General Belgrano and a Type 42 destroyers are still around (or least their batteries) to provide SAM cover and Belgrano's artillery remains operational and in range of Stanley.